Academic literature on the topic 'Parametrized LMIs'

This paper develops a new parameterized approach to the problems of delay-dependent analysis and feedback stabilization for a class of linear continuous-time systems with time-varying delays. An appropriate Lyapunov-Krasovskii functional is constructed to exhibit the delay-dependent dynamics. The construction guarantees avoiding bounding methods and effectively deploying injecting parametrized variables to facilitate systematic analysis. Delay-dependent stability provides a characterization of linear matrix inequalities (LMIs)-based conditions under which the linear time-delay system is asymptotically stable with a γ-level £2 gain. By delay-dependent stabilization, a state-feedback scheme is designed to guarantee that the closed-loop switched system enjoys the delay-dependent asymptotic stability with a prescribed γ-level £2 gain. It is established that the methodology provides the least conservatism in comparison with other published methods. Extension to systems with convex-bounded parameter uncertainties in all system matrices is also provided. All the developed results are tested on representative examples.

This paper considers optimization of rotor system design using stability and vibration response criteria. The initial premise of the study is that the effect of certain design changes can be parametrized in a rotor dynamic model through their influence on the system matrices obtained by finite element modeling. A suitable vibration response measure is derived by considering an unknown axial distribution of unbalanced components having bounded magnitude. It is shown that the worst-case unbalanced response is given by an absolute row-sum norm of the system frequency response matrix. The minimization of this norm is treated through the formulation of a set of linear matrix inequalities that can also incorporate design parameter constraints and stability criteria. The formulation can also be extended to cover uncertain or time-varying system dynamics arising, for example, due to speed-dependent bearing coefficients or gyroscopic effects. Numerical solution of the matrix inequalities is tackled using an iterative method that involves standard convex optimization routines. The method is applied in a case study that considers the optimal selection of bearing support stiffness and damping levels to minimize the worst-case vibration of a flexible rotor over a finite speed range. The main restriction in the application of the method is found to be the slow convergence of the numerical routines that occurs with high-order models and/or high problem complexity.

Background Cardiovascular diseases (CVDs) are the leading cause of mortality globally with almost a third of all annual deaths worldwide. Low- and middle-income countries (LMICs) are disproportionately highly affected covering 80% of these deaths. For CVD, hypertension (HTN) is the leading modifiable risk factor. The comparative impact of diagnostic interventions that improve either the accuracy, the reach, or the completion of HTN screening in comparison to the current standard of care has not been estimated. Methods and findings This microsimulation study estimated the impact on HTN-induced morbidity and mortality in LMICs for four different scenarios: (S1) lower HTN diagnostic accuracy; (S2) improved HTN diagnostic accuracy; (S3) better implementation strategies to reach more persons with existing tools; and, lastly, (S4) the wider use of easy-to-use tools, such as validated, automated digital blood pressure measurement devices to enhance screening completion, in comparison to the current standard of care (S0). Our hypothetical population was parametrized using nationally representative, individual-level HPACC data and the global burden of disease data. The prevalence of HTN in the population was 31% out of which 60% remained undiagnosed. We investigated how the alteration of a yearly blood pressure screening event impacts morbidity and mortality in the population over a period of 10 years. The study showed that while improving test accuracy avoids 0.6% of HTN-induced deaths over 10 years (13,856,507 [9,382,742; 17,395,833]), almost 40 million (39,650,363 [31,34,233, 49,298,921], i.e., 12.7% [9.9, 15.8]) of the HTN-induced deaths could be prevented by increasing coverage and completion of a screening event in the same time frame. Doubling the coverage only would still prevent 3,304,212 million ([2,274,664; 4,164,180], 12.1% [8.3, 15.2]) CVD events 10 years after the rollout of the program. Our study is limited by the scarce data available on HTN and CVD from LMICs. We had to pool some parameters across stratification groups, and additional information, such as dietary habits, lifestyle choice, or the blood pressure evolution, could not be considered. Nevertheless, the microsimulation enabled us to include substantial heterogeneity and stochasticity toward the different income groups and personal CVD risk scores in the model. Conclusions While it is important to consider investing in newer diagnostics for blood pressure testing to continuously improve ease of use and accuracy, more emphasis should be placed on screening completion.

In this paper, we provide new stabilization schemes for a class of linear hybrid time-delay systems under arbitrary switching. These schemes are delay-independent and delay-dependent H∞ stabilization based on proportional-plus-derivative (PPD) feedback strategy. By adopting a selective Lyapunov–Krasovskii functional, new criteria are constructed in a systematic way in terms of feasibility testing of linear matrix inequalities (LMIs). When the time delay is a continuous bounded function, we derive the solution for nominal and polytopic models and identify several existing results as special cases. In case the time delay is a differentiable time-varying function satisfying some bounding relations, we establish a new parametrized LMI characterization for PPD feedback stabilization. The theoretical developments are illustrated on examples of combustion in rocket motor chambers, river pollution control, and resilience analysis, and the ensuing results are compared with the conventional feedback stabilization.

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode theory allow us to use the same type theory to compute and reason in many modal situations, including guarded recursion, axiomatic cohesion, and parametric quantification. We reproduce examples from prior work in guarded recursion and axiomatic cohesion, thereby demonstrating that MTT constitutes a simple and usable syntax whose instantiations intuitively correspond to previous handcrafted modal type theories. In some cases, instantiating MTT to a particular situation unearths a previously unknown type theory that improves upon prior systems. Finally, we investigate the metatheory of MTT. We prove the consistency of MTT and establish canonicity through an extension of recent type-theoretic gluing techniques. These results hold irrespective of the choice of mode theory, and thus apply to a wide variety of modal situations.

La thèse est consacrée au développement d'une méthodologie de stabilité et de stabilisation pour les systèmes linéaires paramètres-dépendants et à retard soumis à la saturation de la commande. Dans le processus industriel, l'amplitude du signal de commande est généralement limitée par les contraintes de sécurité, les limites du cycle physique, etc. Pour cette raison, un outil de synthèse et d'analyse approprié est nécessaire pour décrire avec précision les caractéristiques des systèmes saturés à paramètres linéaires variables. Dans la première partie, une forme dépendante des paramètres de la condition de secteur généralisée (GSC) est considérée pour résoudre le problème de stabilisation saturée. Plusieurs stratégies de contrôle de rétroaction sont étudiées pour stabiliser les systèmes LPV/qLPV saturés. Conditions de stabilisation nécessaires et suffisantes via la formulation d'inégalité matricielle linéaire paramétrée proposée pour les contrôleurs de retour d'état conformes aux exigences de conception (c'est-à-dire l'ensemble admissible des conditions initiales, la région estimée du domaine de convergence asymptotique, la stabilité et les performances robustes sous l'influence des perturbations, etc.). La relaxation des PLMI conçus est illustrée par les résultats de comparaison à l'aide d'une fonction de Lyapunov dépendante des paramètres. Dans la deuxième partie, les développements de stabilité dépendant du délai basés sur la fonctionnelle de Lyapunov-Krasovskii (LKF) sont présentés. Les techniques modernes de limitation avancées sont utilisées avec un équilibre entre conservatisme et complexité de calcul. Ensuite, des analyses de stabilisation de saturation pour les contrôleurs d'ordonnancement de gain. Inspirée des méthodes de système à retard incertain, une nouvelle condition de stabilisation est dérivée de l'analyse de stabilisation dépendante du retard pour le système à retard LPV soumis à des contraintes de saturation. Dans cet aspect, les contrôleurs de rétroaction à programmation de gain stabilisants améliorent les performances et la stabilité du système saturé et fournissent un grand domaine d'attraction. On peut souligner que la formulation dérivée est générale et peut être utilisée pour le contrôle de la conception de nombreux systèmes dynamiques. Enfin, pour maximiser la région d'attraction tout en garantissant la stabilité asymptotique du système en boucle fermée, un problème d'optimisation est inclus dans la stratégie de conception de commande proposée
The dissertation is devoted to developing a methodology of stability and stabilization for the linear parameter-dependent (PD) and time-delay systems (TDSs) subject to control saturation. In the industrial process, control signal magnitude is usually bounded by the safety constraints, the physical cycle limits, and so on. For this reason, a suitable synthesis and analysis tool is needed to accurately describe the characteristics of the saturated linear parameter-varying (LPV) systems. In the part one, a parameter-dependent form of the generalized sector condition (GSC) is considered to solve the saturated stabilization problem. Several feedback control strategies are investigated to stabilize the saturated LPV/qLPV systems. Necessary and sufficient stabilization conditions via the parameterized linear matrix inequality (PLMI) formulation proposed for the feedback controllers conforming to the design requirements (i.e., the admissible set of the initial conditions, the estimated region of the asymptotic convergence domain, the robust stability and performance with the influence of perturbations, Etc.). The relaxation of the designed PLMIs is shown through the comparison results using a parameter-dependent Lyapunov function (PDLF). In the second part, the delay-dependent stability developments based on Lyapunov-Krasovskii functional (LKF) are presented. The modern advanced bounding techniques are utilized with a balance between conservatism and computational complexity. Then, saturation stabilization analyzes for the gain-scheduling controllers. Inspired by uncertain delay system methods, a novel stabilization condition is derived from the delay-dependent stabilizing analysis for the LPV time-delay system subject to saturation constraints. In this aspect, the stabilizing gain-scheduling feedback controllers improve the performance and stability of the saturated system and provide a large attraction domain. It can be emphasized that the derived formulation is general and can be used for the design control of many dynamic systems. Finally, to maximize the attraction region while guaranteeing the asymptotic stability of the closed-loop system, an optimization problem is included to the proposed control design strategy

Este artigo apresenta um controlador Linear com Parâmetros Variáveis (LPV) robusto na estrutura RST (Reference Signal Tracking) para o controle de velocidade de uma Máquina de Relutância Variável (MRV) 6/4. Esta máquina possui um simulador que considera as não linearidades presentes na operação da MRV. A dinâmica da malha de velocidade foi baseada em um modelo ARX LPV identificado para uma determinada faixa de operação a partir de dados coletados em simulação, sendo o nível de corrente normalizado e filtrado o parâmetro variante. Em posse dos parâmetros do modelo, os parâmetros do controlador LPV foram determinados por meio de um problema de otimização convexa, na forma de uma LMI parametrizada (PLMI). Desse modo, foi observado o desempenho do controlador LPV submetido à variação dos parâmetros e comparado com controladores convencionais com parâmetros fixos.