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Статті в журналах з теми "LTI systems with delays":

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Iftar, Altug. "Robust Tracking and Disturbance Rejection for Decentralized Neutral Distributed-time-delay Systems." WSEAS TRANSACTIONS ON SYSTEMS AND CONTROL 18 (October 17, 2023): 307–15. http://dx.doi.org/10.37394/23203.2023.18.31.

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An important problem in control engineering is to design a controller to achieve robust asymptotic tracking of certain reference signals despite certain disturbance inputs. In the present work, this problem, which is known as the robust servomechanism problem, is considered for decentralized linear time-invariant (LTI) neutral systems with distributed time-delay. However, the system is also allowed to have discrete time-delays besides distributed time-delays. The reference signals and the disturbance input are assumed to satisfy a LTI neutral delay-differential equation with distributed and/or discrete time-delays. The necessary and sufficient conditions for the existence of a controller which solves this problem are derived. The structure of this controller (when it exists) is also presented.
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Olgac, Nejat, Ali Fuat Ergenc, and Rifat Sipahi. "“Delay Scheduling”: A New Concept for Stabilization in Multiple Delay Systems." Journal of Vibration and Control 11, no. 9 (September 2005): 1159–72. http://dx.doi.org/10.1177/1077546305055777.

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A trajectory-tracking problem is considered for a linear time invariant (LTI) dynamics with a fixed control law. However, the feedback line is affected by multiple time delays. The stability of the dynamics becomes a complex problem. It is well known that time-delayed LTI systems may exhibit multiple stable operating zones (which we call pockets) in the space of the delays. Our aim in this paper is to locate and experimentally validate these pockets. For the analytical determination of the pockets we utilize a new methodology, the cluster treatment of characteristic roots (CTCR). The study results in several interesting conclusions. (i) The systems may exhibit better control performance (for instance, faster disturbance rejection) for larger time delays. (ii) Consequently, we propose a unique and interesting utilization of the time delays as agents to enhance the control performance, the delay scheduling technique.
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Sipahi, Rifat, and Nejat Olgac. "Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)." Journal of Dynamic Systems, Measurement, and Control 129, no. 3 (August 21, 2006): 245–51. http://dx.doi.org/10.1115/1.2718235.

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A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.
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Kao, C. Y. "On Robustness of Discrete-Time LTI Systems with Varying Time Delays." IFAC Proceedings Volumes 41, no. 2 (2008): 12336–41. http://dx.doi.org/10.3182/20080706-5-kr-1001.02088.

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Kao, Chung-Yao. "On Stability of Discrete-Time LTI Systems With Varying Time Delays." IEEE Transactions on Automatic Control 57, no. 5 (May 2012): 1243–48. http://dx.doi.org/10.1109/tac.2011.2174681.

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Gao, Qingbin, and Nejat Olgac. "Dixon Resultant for Cluster Treatment of LTI Systems with Multiple Delays." IFAC-PapersOnLine 48, no. 12 (2015): 21–26. http://dx.doi.org/10.1016/j.ifacol.2015.09.347.

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Mohajerpoor, Reza, Hamid Abdi, Lakshmanan Shanmugam, and Saeid Nahavandi. "Partial state estimation of LTI systems with multiple constant time-delays." Journal of the Franklin Institute 353, no. 2 (January 2016): 541–60. http://dx.doi.org/10.1016/j.jfranklin.2015.11.011.

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Mesbahi, Afshin, and Mohammad Haeri. "Stable regions in the parameter space of delays for LTI fractional-order systems with two delays." Signal Processing 107 (February 2015): 415–24. http://dx.doi.org/10.1016/j.sigpro.2014.03.012.

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Deng, Yang, Vincent Lechappe, Emmanuel Moulay, and Franck Plestan. "Predictor-Based Control of LTI Remote Systems With Estimated Time-Varying Delays." IEEE Control Systems Letters 5, no. 1 (January 2021): 289–94. http://dx.doi.org/10.1109/lcsys.2020.3001671.

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Alikoc, Baran, and Ali Fuat Ergenc. "A Polynomial Method for Stability Analysis of LTI Systems Independent of Delays." SIAM Journal on Control and Optimization 55, no. 4 (January 2017): 2661–83. http://dx.doi.org/10.1137/16m1077726.

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Дисертації з теми "LTI systems with delays":

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Martínez, Gonzáles Alejandro. "Perturbation Analysis of Eigenvalues for LTI Delay Systems. Regular and Singular Cases." Electronic Thesis or Diss., université Paris-Saclay, 2021. http://www.theses.fr/2021UPASG017.

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Dans ce mémoire, on considère l’analyse des effets induits par les retards sur le comportement des systèmes dynamiques d´écrits par des équations différentielles linéaires à retards incluant des retards discrets dans leur représentation mathématique. Les apports principaux de la thèse concernent la caractérisation du comportement asymptotiques des racines caractéristiques multiples dans deux configurations: un ou deux paramètres (retards). Les résultats proposés et les algorithmes associés permettent de mieux comprendre les mécanismes sous-jacentes (un ou deux retards) et assouplissent les conditions existantes dans la littérature du domaines (deux retards, vus comme paramètres). Pour obtenir de tels critères, l’approche proposée combine le théorème de préparation de Weierstrass avec la méthode du diagramme de Newton. Finalement, ces idées sont également utilisés pour étudier le caractère bien-posé/mal-posé d’un système en boucle fermée en présence d’un contrôleur de type Proportionnel-Dérivé quand la ”dérivé” est approximée en utilisant un opérateur aux différences incluant un retard. Dans ce dernier cas d’étude, les résultats obtenus sont des conditions nécessaires et suffisantes
This dissertation is devoted to the analysis of the effects induced by the delays on the behavior of the dynamical systems described by linear delay-differential equations of retarded type including discrete delays in their mathematical represen-tation. The main contributions of the thesis concern the characterization of the asymptotic behavior of multiple characteristic roots with respect to the delays in two configurations: one or two (delay) parameters. The proposed results and related algorithms give a better understanding of the underlying mechanisms (one or two delay parameters) and relax the existing conditions from the open literature (two delays, seen as parameters). To derive such criteria, the proposed approach combines the Weierstrass Preparation Theorem with the Newton Diagram Method. Finally, such ideas are also used to study the ill-posed/well-posed character of a closed-loop system when the derivative action is approximated by a delay-difference operator. In this last case study, the corresponding derived conditions are necessary and sufficient
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Zhang, Xiping. "Parameter-Dependent Lyapunov Functions and Stability Analysis of Linear Parameter-Dependent Dynamical Systems." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/5270.

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The purpose of this thesis is to develop new stability conditions for several linear dynamic systems, including linear parameter-varying (LPV), time-delay systems (LPVTD), slow LPV systems, and parameter-dependent linear time invariant (LTI) systems. These stability conditions are less conservative and/or computationally easier to apply than existing ones. This dissertation is composed of four parts. In the first part of this thesis, the complete stability domain for LTI parameter-dependent (LTIPD) systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The stability domain is synthesized for both single- and multi-parameter dependent LTI systems. The single-parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity. In the second part of the thesis, a class of parameter-dependent Lyapunov functions is proposed, which can be used to assess the stability properties of single-parameter LTIPD systems in a non-conservative manner. It is shown that stability of LTIPD systems is equivalent to the existence of a Lyapunov function of a polynomial type (in terms of the parameter) of known, bounded degree satisfying two matrix inequalities. The bound of polynomial degree of the Lyapunov functions is then reduced by taking advantage of the fact that the Lyapunov matrices are symmetric. If the matrix multiplying the parameter is not full rank, the polynomial order can be reduced even further. It is also shown that checking the feasibility of these matrix inequalities over a compact set can be cast as a convex optimization problem. Such Lyapunov functions and stability conditions for affine single-parameter LTIPD systems are then generalized to single-parameter polynomially-dependent LTIPD systems and affine multi-parameter LTIPD systems. The third part of the thesis provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of LPV time-delayed systems. It presents both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can be selected to obtain increasingly non-conservative results. Gridding techniques may be used to cast these tests as Linear Matrix Inequalities (LMI's). In cases when the system matrices depend affinely or quadratically on the parameter, gridding may be avoided. These LMI's can be solved efficiently using available software. A numerical example of a time-delayed system motivated by a metal removal process is used to demonstrate the theoretical results. In the last part of the thesis, topics for future investigation are proposed. Among the most interesting avenues for research in this context, it is proposed to extend the existing stability analysis results to controller synthesis, which will be based on the same Lyapunov functions used to derive the nonconservative stability conditions. While designing the dynamic ontroller for linear and parameter-dependent systems, it is desired to take the advantage of the rank deficiency of the system matrix multiplying the parameter such that the controller is of lower dimension, or rank deficient without sacrificing the performance of closed-loop systems.
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Zekraoui, Salim. "Contrôle et estimation en temps fini de certaines classes d'EDP." Electronic Thesis or Diss., Centrale Lille Institut, 2023. http://www.theses.fr/2023CLIL0028.

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L'objectif principal de cette thèse est d'explorer et d'analyser les problèmes d'estimation et destabilisation non-asymptotique (en temps fini, fixe, et prescrit) de certaines classes de systèmes de dimensioninfinie, notamment les systèmes linéaires invariants en temps avec retards (ponctuels ou distribués) d'entrée oude sortie et les équations aux dérivées partielles (EDP) de type réaction-diffusion. Comme les résultats existantssur ces classes de systèmes sont peu nombreux, nous commençons par revoir les concepts et les résultats sur lesoutils non asymptotiques pour les systèmes de dimension infinie. Ensuite, nous étendons ces outils pour les systèmesde dimension infinie. Dans ce contexte, nous commençons par le problème de compensation, en temps fini/fixe,des retards d'entrée et de sortie pour les systèmes LTI en utilisant la méthode du backstepping pour les EDP(avec des transformations inversibles non-linéaires et/ou variant en temps). Pour appliquer cette approche, nousreformulons le système considéré en une cascade de système EDO-EDP où la partie EDP est une équation detransport hyperbolique qui modélise l'effet du retard sur l'entrée/sortie. Ensuite, nous traitons le problème dela stabilisation frontière en temps fini/fixe d'une classe des EDP de réaction-diffusion. À notre connaissance,ce problème est resté ouvert dans la littérature pendant une période considérable. Nous abordons ce problèmecomplexe à l'aide de méthodes classiques liées aux Fonctions de Lyapunov de Contrôle (CLF). Nous donnonsquelques indications sur l'extension de cette approche au problème de stabilisation entrée-état (ISS) et au problèmedu suivi en temps fini/fixe pour les EDP de réaction-diffusion. Nous soulignons les limitations de notre méthodepour la conception des observateurs. Enfin, nous abordons le problème de la compensation, en temps prescrit, desretards d'entrée des systèmes de réaction-diffusion par une commande par retour d'état basée sur un observateur enutilisant la méthode du backstepping pour les EDP. Ce problème est difficile, car il nécessite de traiter la conceptiondes observateurs et des contrôleurs avec des gains variant en temps qui tendent vers l'infini lorsque le temps serapproche du temps prescrit de convergence
This Ph.D. thesis is devoted to the problems of non-asymptotic (finite, fixed, prescribed-time) estimation and stabilization of some classes of infinite-dimensional systems, namely LTI systems subject to input/sensor (pointwise or distributed) delays and reaction-diffusion PDEs. As the existing results on these classes of systems are few, we begin by reviewing relevant concepts and results on non-asymptotic tools (including homogeneity-based tools and time-varying tools) for finite-dimensional systems. Afterward, we extend these tools to infinite-dimensional settings. Firstly, we start with the problem of input and sensor delay compensation in finite/fixed/prescribed time of LTI systems where we use the so-called backstepping approach for PDEs (with some nonlinear and/or time-varying invertible transformations). To apply this approach, we reformulate the considered LTI system into a cascade ODE-PDE system where the PDE part is a hyperbolic transport equation that models the effect of the delay on the input/output. Secondly, we consider the problem of boundary state-dependent finite/fixed-time stabilization of reaction-diffusion PDEs. To the best of our knowledge, this problem has remained open in the literature for a considerable long time. We tackle this challenging problem using classical methods related to Control Lyapunov functions. We provide some hints on how we to extend this approach to input-to-state stabilization and non-asymptotic tracking problem for reaction-diffusion PDEs. We point out the limitations of our approach to observer design. Finally, we tackle the problem of input delay compensation of reaction-diffusion systems in prescribed time by output feedback using the backstepping approach. This problem is challenging, as one deals with observer and control designs with some time-varying gains that go to infinity when the time gets closer to the prescribed time of convergence, which brings additional challenges and issues. Dealing with these challenges requires introducing novel infinite-dimensional time-varying backstepping transformations in conjunction with advanced predictor-based concepts adapted to parabolic PDEs
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Sereni, Bruno. "Static output feedback control for LPV and uncertain LTI systems /." Ilha Solteira, 2019. http://hdl.handle.net/11449/180732.

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Orientador: Edvaldo Assunção
Resumo: Este trabalho aborda o controle via realimentação estática de saída aplicado à sistemas lineares com parâmetro variante (LPV) e lineares incertos invariantes no tempo (LIT). O projeto de ganhos de realimentação estática de saída apresentado neste trabalho é baseado no método dos dois estágios, o qual consiste em primeiramente obter um ganho de realimentação de estados, e então, utilizar esta informação no segundo estágio para obter-se o ganho de realimentação estática de saída desejado. As soluções para os problemas investigados são apresentadas na forma de desigualdades matriciais lineares (no inglês, linear matrix inequalities, LMIs), obtidas por meio da aplicação do Lema de Finsler. Baseado em resultados anteriores encontrados na literatura, este trabalho propõe uma estratégia de relaxação de forma a obter um método menos conservador para obtenção de ganhos robustos de realimentação estática de saída para sistemas incertos LTI. Na estratégia proposta, as variáveis adicionais do Lema de Finsler são consideradas como dependentes de parâmetro, juntamente com o uso de funções de Lyapunov dependentes de parâmetro (no inglês, parameter-dependent Lyapunov functions, PDLFs). É apresentado um estudo avaliando a eficácia da estratégia proposta em fornecer uma maior região de factibilidade para um dado problema. Os resultados foram utilizados em uma comparação com um método de relaxação baseado apenas no uso de PDLFs. Uma segunda contribuição deste trabalho consiste na proposta de um... (Resumo completo, clicar acesso eletrônico abaixo)
Abstract: The static output feedback (SOF) control applied to linear parameter-varying (LPV) and uncertain linear time-invariant (LTI) systems are addressed in this work. The approach chosen for the design of SOF gains is based on the two-stage method, which consists in obtaining a state feedback gain at first, and then using that information for deriving the desired SOF gain at the second stage. The solutions for the investigated problems are presented in terms of linear matrix inequalities (LMIs), obtained by means of the application of the Finsler's Lemma. Based on previous papers found in literature, this work proposes a relaxation strategy in order to achieve a less conservative method for obtaining robust SOF gains for uncertain LTI systems. In the proposed strategy, the Finsler's Lemma additional variables are considered to be parameter-dependent along with the use of parameter-dependent Lyapunov functions (PDLFs). A study evaluating the effectiveness of the proposed strategy in providing a larger feasibility region for a given problem is presented. The results were used in a comparison with a relaxation method based only on PDLFs. Another contribution of this work lies in the proposal of a solution for the control of LPV systems via the design of a gain-scheduled SOF controller. The methods proposed for both control problems were applied on the design of controllers for an active suspension system. In the experiments, it was assumed that only one of its four system's states wer... (Complete abstract click electronic access below)
Mestre
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Zhong, Qingchang. "Robust control of systems with delays." Thesis, Imperial College London, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405412.

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Ashoori, Ahmad. "Analysis of motor performance in Parkinson's disease through LTI dynamical systems." Thesis, University of British Columbia, 2014. http://hdl.handle.net/2429/51518.

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Motor performance in Parkinson's disease is marked by a variety of impairments, and is indicative of faulty feedback mechanisms in the brain that arise due to a lack of dopamine. Quantifying motor performance as well as investigating the correlation of motor behaviour and clinical measures has been sought as in important avenue to study disease pathophysiology. We propose the use of linear dynamical systems to finely characterize motor performance, and for possible interpretations of neurological phenomena, such as compensatory mechanisms that can be cast in the framework of control theory. While coarse measurements of motor performance exist (e.g., maximum velocity, mean velocity, root mean square error), they often cannot distinguish between qualitatively different types of movement. (Consider for example, the wide variety of step response behaviors possible in second order systems which may have the same settling time, but a wide range of damping ratios.) In contrast, LTI models provide a dynamical mapping of the sensorimotor transformation required in tracking tasks. Model parameters of linear dynamical systems (such as damping ratio, and natural frequency) can more readily describe qualitatively similar motor phenomenon than existing coarse measurements. From time-series data of various manual tracking experiments, we first perform a set of preprocessing techniques dependent on the particular experimental setup. The pre-processing techniques have been carefully evaluated to appropriately address possible noise, nonlinearities, and other data irregularities. We then apply existing tools for system identification (e.g., ARX, ARMAX, subspace methods) to identify numerically robust second-order LTI system models. The choice of system identification method (as well as choice of pre-processing techniques) is critical in determining the variability in the resulting model parameters. We identify parameters of the LTI models which are amenable to comparison across subjects (and across groups), and evaluate their statistical significance. The main contributions of this thesis are: - Selection of pre-processing and system identification techniques for three experimental setups for manual tracking experiments - Control theoretic framework for tremor as a compensatory mechanism that is advantageous in some tracking tasks - Sensor-based assessment of rigidity via decay rate - Assessment of cognitive inflexibility through mode detection and delay
Applied Science, Faculty of
Electrical and Computer Engineering, Department of
Graduate
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Yedes-Bougatef, Naima. "Commande sous contraintes des systèmes discrets périodiques." Thesis, Poitiers, 2012. http://www.theses.fr/2012POIT2305/document.

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Cette thèse se situe dans le cadre de l’analyse et de la synthèse des systèmes périodiques. Les contributions présentées dans ce mémoire portent sur la commande sous contraintes des systèmes linéaires discrets périodiques. Ces contraintes, portant sur l’état du système et/ ou sur la commande, peuvent être des contraintes de positivité ou de bornitude. Dans ce travail, des conditions d’analyse en stabilité et positivité des systèmes périodiques en termes de LMI (Inégalité Matricielle Linéaire) strictes, sont présentées. Ces outils d’analyse ont ensuite permis d’élaborer une loi de commande par retour d’état périodique. Les résultats obtenus sont exploités par la suite pour développer une commande par retour d’état périodique robuste pour les systèmes périodiques incertains. Des conditions de stabilisation robuste sont élaborées en utilisant la S-procédure. En outre, des conditions de stabilité et stabilisation par retour d’état périodique des systèmes périodiques avec retards sont établies. Le problème de stabilisation de ce type de systèmes sous un certain nombre de contraintes est résolu en suivant deux approches, la première est basée sur les techniques de Lyapunov la seconde fait appel à la programmation linéaire. Outre la notion de stabilité, la notion de performance des systèmes en boucle fermée est traitée. Pour cela, nous proposons une commande de type H∞ pour résoudre le problème de rejet de perturbations
This thesis deals with the analysis and the control problem of periodic linear discrete systems (PLDS). The contributions presented in this work focuses on the constrained control of PLDS. Conditions for stability analysis and positivity are established in terms of strict LMI (Linear Matrix Inequalities). The stabilization of PLDS under the condition that the closed-loop system is positive and stable is addressed as well as the case of bounded state and/ or control variables. The obtained results are then extended to the synthesis of robust state feedback controllers, where some of which are based on the S − procedure technique. Furthermore, some conditions of stability and stabilization of PLDS with delays are established. The problem of stabilization of constrained PLDS is addressed based on the Lyapunov techniques or the Linear Programming techniques. The robust H∞ state feedback control in which both robust stability and a prescribed H∞ performance are required is investigated
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Liacu, Bogdan Cristian. "Network-based Haptic Systems with Time-Delays." Phd thesis, Supélec, 2012. http://tel.archives-ouvertes.fr/tel-00771948.

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During the last decades, virtual environments have become very popular and are largely used in many domains as, for example, prototyping, trainings for different devices, assistance in completing difficult tasks, etc. The interaction with the virtual reality, as well as the feedback force, is assured by haptic interfaces. Generally, such systems are affected by communication and processing time-delays, resulting in a deterioration of performances. In this thesis, a complete study of the existing methods, as well as theoretical tools and new solutions, are proposed for the haptic framework. First, a comparative study, based on the experimental results obtained on a 1-dof haptic system, highlights the advantages and drawbacks of the most common control algorithms ported from teleoperation to haptics. Next, the theoretical tools needed in analyzing the stability of the delayed systems in different situations, as well as the physical limitations of the experimental platforms considered, are examined. Besides the standard case of constant time-delays, uncertainties are also considered and modeled by different types of distributions (uniform, normal and gamma distribution with gap). In the sequel, for overcoming the drawback of time-delays, two new approaches are proposed. First, the use of Smith predictor-based control is addressed and a specific solution for haptic systems is developed and discussed. The main idea is to introduce into the Smith predictor the environmental forces by using the additional information from the virtual reality regarding the distances between the controlled virtual object and other objects in the scene. To overcome the loss of performances induced by using a fixed gain in the controllers for all situations (free or restricted motions), the second approach proposes a gain-scheduling Proportional Derivative control strategy depending on the distance until a possible collision. Both approaches are experimentally validated on a 3-dof haptic platform, under different scenarios elaborated gradually from simple situations - free and restricted motion, contacts with moving objects, to more complex situations - virtual box with fixed or moving sides.
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Rahman, Bootan Mohammed. "Dynamics of neural systems with time delays." Thesis, University of Sussex, 2017. http://sro.sussex.ac.uk/id/eprint/67773/.

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Complex networks are ubiquitous in nature. Numerous neurological diseases, such as Alzheimer's, Parkinson's, epilepsy are caused by the abnormal collective behaviour of neurons in the brain. In particular, there is a strong evidence that Parkinson's disease is caused by the synchronisation of neurons, and understanding how and why such synchronisation occurs will bring scientists closer to the design and implementation of appropriate control to support desynchronisation required for the normal functioning of the brain. In order to study the emergence of (de)synchronisation, it is necessary first to understand how the dynamical behaviour of the system under consideration depends on the changes in systems parameters. This can be done using a powerful mathematical method, called bifurcation analysis, which allows one to identify and classify different dynamical regimes, such as, for example, stable/unstable steady states, Hopf and fold bifurcations, and find periodic solutions by varying parameters of the nonlinear system. In real-world systems, interactions between elements do not happen instantaneously due to a finite time of signal propagation, reaction times of individual elements, etc. Moreover, time delays are normally non-constant and may vary with time. This means that it is vital to introduce time delays in any realistic model of neural networks. In this thesis, I consider four different models. First, in order to analyse the fundamental properties of neural networks with time-delayed connections, I consider a system of four coupled nonlinear delay differential equations. This model represents a neural network, where one subsystem receives a delayed input from another subsystem. The exciting feature of this model is the combination of both discrete and distributed time delays, where distributed time delays represent the neural feedback between the two sub-systems, and the discrete delays describe neural interactions within each of the two subsystems. Stability properties are investigated for different commonly used distribution kernels, and the results are compared to the corresponding stability results for networks with no distributed delays. It is shown how approximations to the boundary of stability region of an equilibrium point can be obtained analytically for the cases of delta, uniform, and gamma delay distributions. Numerical techniques are used to investigate stability properties of the fully nonlinear system and confirm our analytical findings. In the second part of this thesis, I consider a globally coupled network composed of active (oscillatory) and inactive (non-oscillatory) oscillators with distributed time delayed coupling. Analytical conditions for the amplitude death, where the oscillations are quenched, are obtained in terms of the coupling strength, the ratio of inactive oscillators, the width of the uniformly distributed delay and the mean time delay for gamma distribution. The results show that for uniform distribution, by increasing both the width of the delay distribution and the ratio of inactive oscillators, the amplitude death region increases in the mean time delay and the coupling strength parameter space. In the case of the gamma distribution kernel, we find the amplitude death region in the space of the ratio of inactive oscillators, the mean time delay for gamma distribution, and the coupling strength for both weak and strong gamma distribution kernels. Furthermore, I analyse a model of the subthalamic nucleus (STN)-globus palidus (GP) network with three different transmission delays. A time-shift transformation reduces the model to a system with two time delays, for which the existence of a unique steady state is established. Conditions for stability of the steady state are derived in terms of system parameters and the time delays. Numerical stability analysis is performed using traceDDE and DDE-BIFTOOL in Matlab to investigate different dynamical regimes in the STN-GP model, and to obtain critical stability boundaries separating stable (healthy) and oscillatory (Parkinsonian-like) neural ring. Direct numerical simulations of the fully nonlinear system are performed to confirm analytical findings, and to illustrate different dynamical behaviours of the system. Finally, I consider a ring of n neurons coupled through the discrete and distributed time delays. I show that the amplitude death occurs in the symmetric (asymmetric) region depending on the even (odd) number of neurons in the ring neural system. Analytical conditions for linear stability of the trivial steady state are represented in a parameter space of the synaptic weight of the self-feedback and the coupling strength between the connected neurons, as well as in the space of the delayed self-feedback and the coupling strength between the neurons. It is shown that both Hopf and steady-state bifurcations may occur when the steady state loses its stability. Stability properties are also investigated for different commonly used distribution kernels, such as delta function and weak gamma distributions. Moreover, the obtained analytical results are confirmed by the numerical simulations of the fully nonlinear system.
10

Baldan, Giancarlo. "Low complexity quantized controllers for LTI systems : peak-to-peak performance guarantees." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/103717.

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Анотація:
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 139-143).
In this thesis, we propose a novel feedback control scheme for unstable LTI systems performing noise attenuation via a finite-rate digital channel. In the first part of the thesis, we introduce the structure of the control system as well as the encoder and decoder used to transmit the required control signals along the digital channel. The performances of the proposed algorithm are then evaluated by providing explicit bounds on the peak-to-peak noise attenuation, in regards to the induced l[subscript infinity symbol] gain of the closed loop . This result is obtained by constructing a new class of storage functions that can be employed to verify the dissipativity of the closed loop system with respect to a suitable supply rate function. In the second part of the thesis, we examine the trade-off between the closed loop performances and the required rate of the channel. While the digital channel imposes some limitations on the achievable induced l[subscript infinity symbol] gain, we show how the performances of the proposed scheme can still approximate those achievable without communication constraints provided that the rate of the channel is large enough. A numerical optimization problem is then devised to design the parameters of the control scheme in order to minimize the strain on the channel while matching some prescribed constraints on the closed loop induced l[subscript infinity symbol] gain.
by Giancarlo Baldan.
Ph. D.

Книги з теми "LTI systems with delays":

1

Sipahi, Rifat. Mastering Frequency Domain Techniques for the Stability Analysis of LTI Time Delay Systems. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2019. http://dx.doi.org/10.1137/1.9781611975727.

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2

Kim, A. V., and A. V. Ivanov. Systems with Delays. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119117841.

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3

Li, Xiaodi, and Shiji Song. Impulsive Systems with Delays. Singapore: Springer Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-4687-4.

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4

Seuret, Alexandre, Laurentiu Hetel, Jamal Daafouz, and Karl H. Johansson, eds. Delays and Networked Control Systems. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32372-5.

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5

Kim, A. V. Systems with delays: Analysis, control, and computations. Hoboken, New Jersey: John Wiley & Sons, Inc., 2015.

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6

Park, Ju H., Tae H. Lee, Yajuan Liu, and Jun Chen. Dynamic Systems with Time Delays: Stability and Control. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-9254-2.

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7

Garza, Dave. LTI custom curriculum lab manual HV120: Energy efficiency and green technology systems. Clifton Park, N.Y: Delmar Cengage Learning, 2013.

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8

Xia, Yuanqing, Mengyin Fu, and Peng Shi. Analysis and Synthesis of Dynamical Systems with Time-Delays. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-02696-6.

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9

Wu, Zheng-Guang, Hongye Su, Peng Shi, and Jian Chu. Analysis and Synthesis of Singular Systems with Time-Delays. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-37497-5.

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10

Wu, Zheng-Guang. Analysis and Synthesis of Singular Systems with Time-Delays. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Частини книг з теми "LTI systems with delays":

1

Qi, Tian, Jing Zhu, and Jie Chen. "Delay Margin for Robust Stabilization of LTI Delay Systems." In Delays and Interconnections: Methodology, Algorithms and Applications, 281–98. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-11554-8_18.

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2

Alikoç, Baran, and Ali Fuat Ergenç. "A New Delay-Independent Stability Test for LTI Systems with Single Delay." In Advances in Delays and Dynamics, 63–76. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53426-8_5.

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3

Sipahi, Rifat. "Design of Imaginary Spectrum of LTI Systems with Delays to Manipulate Stability Regions." In Advances in Delays and Dynamics, 127–40. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-53426-8_9.

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4

Qiao, Wei, and Rifat Sipahi. "Graph Laplacian Design of a LTI Consensus System for the Largest Delay Margin: Case Studies." In Delay Systems, 101–12. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-01695-5_8.

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5

Yin, Lizi, and Dianwu Yang. "LMI Conditions for Stability of Impulsive Stochastic Neural Networks with Unbounded Time-Varying Delays." In Web Information Systems and Mining, 434–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23971-7_55.

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6

Sayood, Khalid. "Properties of LTI Systems." In Signals and Systems, 75–84. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-031-02545-7_8.

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7

Yu, Chengpu, Lihua Xie, Michel Verhaegen, and Jie Chen. "Identification of LTI Systems." In Blind Identification of Structured Dynamic Systems, 49–70. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-7574-4_4.

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8

Yaniv, Oded. "Synthesis of LTI Controllers for MISO LTI Plants." In Quantitative Feedback Design of Linear and Nonlinear Control Systems, 59–91. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-6331-7_3.

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9

Yaniv, Oded. "Synthesis of LTI Controllers for MIMO LTI Plants." In Quantitative Feedback Design of Linear and Nonlinear Control Systems, 93–243. Boston, MA: Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-6331-7_4.

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10

Gupta, Pushpendra Kumar, and V. Krishna Rao Kandanvli. "New LMI Criterion to the Robust Stability of Discrete-Time Systems with Time-Varying Delays and Generalized Overflow Nonlinearities." In Lecture Notes in Electrical Engineering, 213–27. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-6840-4_17.

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Тези доповідей конференцій з теми "LTI systems with delays":

1

Cavdaroglu, Mursel Emre, and Nejat Olgac. "Full State Feedback Control Design for “Delay Scheduling”." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2127.

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A fixed full state feedback controller design approach is proposed for linear time invariant (LTI) systems with time delays. This approach enables the designer to use recently introduced “delay scheduling” procedure, which opens a new direction in control synthesis. “Delay scheduling” strategy suggests prolonging the existing (and unavoidable) delays in order to recover stability or to improve the control performance features. To be able to do this, however, system should have multiple stable operating zones in the domain of the delays. The main contribution of this paper is to develop a procedure for designing such a control law. It starts with a simple usage of LQR for non-delayed systems. This approach, nevertheless, imparts some complexities when delays are introduced. We handle them using a recent paradigm, called the Cluster Treatment of Characteristic Roots (CTCR). For an example to the ensuing design strategy, we use a fully actuated cart-pendulum system. Relevant simulations are carried out to show the viability of the proposed idea.
2

Sipahi, Rifat, and Nejat Olgac. "Stability Analysis of Multiple Time Delayed Systems Using the Direct Method." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41495.

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A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.
3

Sipahi, Rifat, and Payam Mahmoodi Nia. "Controller Design With Fixed Delay-Margin for a LTI Unstable Open-Loop Plant: Case Studies." In ASME 2014 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/dscc2014-6325.

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Around a benchmark open-loop unstable LTI plant with a single delay, we design controllers that create marginal stability of the closed loop at a pre-defined delay margin value τ. These controllers therefore guarantee system stability for all delays less than τ. Case studies covering various scenarios are presented.
4

Shaobu Wang, Quanyuan Jiang, and Yiqun Miao. "Delay-dependent stability criteria for LTI systems with multiple time delays." In 2009 Chinese Control and Decision Conference (CCDC). IEEE, 2009. http://dx.doi.org/10.1109/ccdc.2009.5195212.

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5

Qiao, Wei, and Rifat Sipahi. "Responsible-Eigenvalue Control for Creating Autonomy in Coupled Systems With Delays." In ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control. ASMEDC, 2011. http://dx.doi.org/10.1115/dscc2011-6054.

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A class of linear time-invariant (LTI) consensus system with multiple agents and identical communication delays among the agents is considered. For this type of system, we recently showed that a responsible eigenvalue (RE) exists determining the amount of delay (delay margin) that the system can withstand without losing stability. In this paper, we use RE to design controllers such that the delay margin of the system increases as the agents make autonomous decisions. This Responsible Eigenvalue-control enables real-time tuning of RE in a way that the system becomes robust against delays. A numerical example demonstrates intriguing results that connect for the first time in the literature the controller design, the features of the associated graph Laplacian, and RE concept.
6

Gao, Qingbin, Umut Zalluhoglu, and Nejat Olgac. "Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)." In ASME 2013 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/dscc2013-3703.

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It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.
7

Deng, Yang, Vincent Lechappe, Emmanuel Moulay, and Franck Plestan. "Prediction-based control with delay estimation of LTI systems with input-output delays." In 2019 American Control Conference (ACC). IEEE, 2019. http://dx.doi.org/10.23919/acc.2019.8814876.

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8

Elbeyli, Ozer, and J. Q. Sun. "Efficiency and Accuracy of Semi-Discretization Schemes for Time Delayed Feedback Control Systems." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-42759.

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Semi-discretization is an effective method for analysis and control design of time-invariant as well as periodic linear systems with time delay. This paper briefly describes various approximation schemes in conjunction to the semi-discretization method. Comparison measures making use of the stability bounds of control gains and the controlled response of the system are presented. The accuracy and efficiency of the method with the zeroth order, improved zeroth order and first order approximations are compared through numerical simulations. Another first order approximation of the system with multiple time delays under a non-delayed feedback leads to integro-differential equations where a simple approximation is utilized to generate discrete maps. It is found that the first order approximation provides substantial improvements in accuracy and efficiency for feedback control design of LTI and periodic systems.
9

Negi, Nandini, and Aranya Chakrabortty. "Sparse Optimal Control of LTI Systems under Sparsity-Dependent Delays." In 2018 Annual American Control Conference (ACC). IEEE, 2018. http://dx.doi.org/10.23919/acc.2018.8431138.

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10

Tsubakino, Daisuke, Tiago Roux Oliveira, and Miroslav Krstic. "Predictor-feedback for multi-input LTI systems with distinct delays." In 2015 American Control Conference (ACC). IEEE, 2015. http://dx.doi.org/10.1109/acc.2015.7170796.

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Звіти організацій з теми "LTI systems with delays":

1

Vaidyanathan, P. P. Cyclic LTI Systems in Digital Signal Processing. Fort Belvoir, VA: Defense Technical Information Center, June 1998. http://dx.doi.org/10.21236/ada349622.

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2

Vaidyanathan, P. P., and Ahmet Kirac. Cyclic LTI Systems and the Paraunitary Interpolation Problem. Fort Belvoir, VA: Defense Technical Information Center, January 1998. http://dx.doi.org/10.21236/ada342273.

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3

Teo, Justin, and Jonathan P. How. Gradient Projection Anti-windup Scheme on Constrained Planar LTI Systems. Fort Belvoir, VA: Defense Technical Information Center, March 2010. http://dx.doi.org/10.21236/ada523139.

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4

Santarelli, Keith R. A switched state feedback law for the stabilization of LTI systems. Office of Scientific and Technical Information (OSTI), September 2009. http://dx.doi.org/10.2172/993891.

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5

Kushner, Harold J. Numerical Approximations for Nonlinear Stochastic Systems With Delays. Fort Belvoir, VA: Defense Technical Information Center, August 2004. http://dx.doi.org/10.21236/ada459437.

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6

Chen, Guang. Multi-agent Collaborative Perception for Autonomous Driving: Unsettled Aspects. 400 Commonwealth Drive, Warrendale, PA, United States: SAE International, August 2023. http://dx.doi.org/10.4271/epr2023017.

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<div class="section abstract"><div class="htmlview paragraph">This report delves into the field of multi-agent collaborative perception (MCP) for autonomous driving: an area that remains unresolved. Current single-agent perception systems suffer from limitations, such as occlusion and sparse sensor observation at a far distance.</div><div class="htmlview paragraph"><b>Multi-agent Collaborative Perception for Autonomous Driving: Unsettled Aspects</b> addresses three unsettled topics that demand immediate attention: <ul class="list disc"><li class="list-item"><div class="htmlview paragraph">Establishing normative communication protocols to facilitate seamless information sharing among vehicles</div></li><li class="list-item"><div class="htmlview paragraph">Definiting collaboration strategies, including identifying specific collaboration projects, partners, and content, as well as establishing the integration mechanism</div></li><li class="list-item"><div class="htmlview paragraph">Collecting sufficient data for MCP model training, including capturing diverse modal data and labeling various downstream tasks as accurately as possible</div></li></ul></div><div class="htmlview paragraph"><a href="https://www.sae.org/publications/edge-research-reports" target="_blank">Click here to access the full SAE EDGE</a><sup>TM</sup><a href="https://www.sae.org/publications/edge-research-reports" target="_blank"> Research Report portfolio.</a></div></div>
7

Megersa, Kelbesa. Alternative Systems for Managing Financial Transactions in Humanitarian Crises. Institute of Development Studies (IDS), April 2021. http://dx.doi.org/10.19088/k4d.2021.136.

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Restrictions on the banking sector are having a growing adverse impact on the flow of funds to humanitarian agencies and assisting communities affected by humanitarian crises has also become much more difficult and costly. Delays, refusals of transactions by financial institutions and outright bank account closures worsen humanitarian crises by delaying aid distribution response times. The inability to channel funds and critical financial services into countries in humanitarian crisis prevents life-saving humanitarian assistance from reaching those who need it most. The absence of legal transfer channels means the financing vacuum is often filled by illicit means, which can facilitate the spread of crime and corruption (ODI, 2021). Humanitarian organisations have turned to a variety of transaction channels due to disruptions in legitimate transfer mechanisms. Without these alternative money transfer channels humanitarian organisations have been unable to run some parts of their programming. These alternatives means of obtaining funds requires humanitarian organisations to enter into less regulated financial agreements that are not subject to international standards.
8

Roberts, R. G., C. A. Moore, S. Tosunoglu, and D. W. Repperger. Wave Variable Method to Control Force-Reflecting Teleoperators With Time Delays: Generalizing the Wave Variable Method to Multiple Degree-of-Freedom Systems. Fort Belvoir, VA: Defense Technical Information Center, March 2005. http://dx.doi.org/10.21236/ada433539.

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9

Ciapponi, Agustín. Does physician-led triage reduce emergency department overcrowding? SUPPORT, 2016. http://dx.doi.org/10.30846/1610112.

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Emergency department overcrowding is a serious problem facing healthcare systems worldwide that can lead to delays in time-sensitive diagnostic and treatment decisions and poor health outcomes. Triage systems are used to decide who needs urgent care and who can wait, sorting patients according to urgency or type of service required. They employ systems to prioritise or assign patients to treatment categories in order to assist in their management.
10

Chen, Chiung-Chu, and Michael McQuaid. A Thermochemical Kinetic-Based Study of Ignition Delays for 2-Azidoethanamine-Red Fuming Nitric Acid Systems: 2-Azido-N-Methylethanamine (MMAZ) Vs. 2-Azido-N,N-Dimethylethanamine (DMAZ). Fort Belvoir, VA: Defense Technical Information Center, January 2014. http://dx.doi.org/10.21236/ada599206.

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