Дисертації з теми "Stability intervals"

Reaction-diffusion equations have been used to study various phenomena across different fields. These equations can be posed on the whole real line, or on a subinterval, depending on the situation being studied. For finite intervals, we also impose diverse boundary conditions on the system. In the present thesis, we solely focus on the bistable reaction-diffusion equation while working on a bounded interval of the form $[0,L]$ ($L>0$). Furthermore, we consider both mixed and no-flux boundary conditions, where we extend the former to Dirichlet boundary conditions once our analysis of that system is complete. We first use phase-plane analysis to set up our initial investigation of both systems. This gives us an integral describing the transit time of orbits within the phase-plane. This allows us to determine the bifurcation diagram of both systems. We then transform the integral to ease numerical calculations. Finally, we determine the stability of the steady states of each system.

Cette thèse est construite autour de deux types d'estimation de l'état d'un système, traités séparément. Le premier problème abordé concerne la construction d'observateurs positifs basés sur la métrique de Hilbert. Le second traite de la synthèse d'observateurs par intervalles pour différentes familles de systèmes dynamiques et la construction de lois de commande robustes qui stabilisent ces systèmes.Un système positif est un système dont les variables d'état sont toujours positives ou nulles lorsque celles-ci ont des conditions initiales qui le sont. Les systèmes positifs apparaissent souvent de façon naturelle dans des applications pratiques où les variables d'état représentent des quantités qui n'ont pas de signification si elles ont des valeurs négatives. Dans ce contexte, il parait naturel de rechercher des observateurs fournissant des estimées elles aussi positives ou nulles. Dans un premier temps, notre contribution réside dans la mise au point d'une nouvelle méthode de construction d'observateurs positifs sur l'orthant positif. L'analyse de convergence est basée sur la métrique de Hilbert. L'avantage concurrentiel de notre méthode est que la vitesse de convergence peut être contrôlée.Notre étude concernant la synthèse d'observateurs par intervalles est basée sur la théorie des systèmes dynamiques positifs. Les observateurs par intervalles constituent un type d'observateurs très particuliers. Ce sont des outils développés depuis moins de 15 ans seulement : ils trouvent leur origine dans les travaux de Gouzé et al. en 2000 et se développent très rapidement dans de nombreuses directions. Un observateur par intervalles consiste en un système dynamique auxiliaire fournissant un intervalle dans lequel se trouve l'état, en considérant que l'on connait des bornes pour la condition initiale et pour les quantités incertaines. Les observateurs par intervalles donnent la possibilité de considérer le cas où des perturbations importantes sont présentes et fournissent certaines informations à tout instant
This thesis presents new results in the field of state estimation based on the theory of positive systems. It is composed of two separate parts. The first one studies the problem of positive observer design for positive systems. The second one which deals with robust state estimation through the design of interval observers, is at the core of our work.We begin our thesis by proposing the design of a nonlinear positive observer for discrete-time positive time-varying linear systems based on the use of generalized polar coordinates in the positive orthant. For positive systems, a natural requirement is that the observers should provide state estimates that are also non-negative so they can be given a physical meaning at all times. The idea underlying the method is that first, the direction of the true state is correctly estimated in the projective space thanks to the Hilbert metric and then very mild assumptions on the output map allow to reconstruct the norm of the state. The convergence rate can be controlled.Later, the thesis is continued by studying the so-called interval observers for different families of dynamic systems in continuous-time, in discrete-time and also in a context "continuous-discrete" (i.e. a class of continuous-time systems with discrete-time measurements). Interval observers are dynamic extensions giving estimates of the solution of a system in the presence of various type of disturbances through two outputs giving an upper and a lower bound for the solution. Thanks to interval observers, one can construct control laws which stabilize the considered systems

We consider a finite section (Galerkin) and a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polymoninals, where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra techniques, where also the system case is mentioned. With the help of appropriate Sobolev spaces a result on convergence rates is proved. Computational aspects are discussed in order to develop an effective algorithm. Numerical results, also for a class of nonlinear singular integral equations, are presented.

We consider a collocation method for Cauchy singular integral equations on the interval based on weighted Chebyshev polynomials , where the coefficients of the operator are piecewise continuous. Stability conditions are derived using Banach algebra methods, and numerical results are given.

The main research objective in this thesis is to investigate the stability and performance of the interval type-2 (IT2) polynomial-fuzzy-model-based (PFMB) control system. PFMB control scheme has been developed recently around 2009 and demonstrates more potential than the traditional Takagi-Sugeno fuzzy-model-based (T-S FMB) control approach to represent the nonlinearities in the plant. Meanwhile, the IT2 fuzzy logic has also been proposed to incorporate uncertainties of the nonlinear systems into the membership functions directly. Through the IT2 PFMB control design approach, both the nonlinearity and the uncertainty in the system can be handled well. The control performance and the relaxation of stability conditions of IT2 PFMB control systems are studied and investigated in the thesis. The main contribution of the thesis is summarized in three tasks and presented as following: In the first task in Chapter 3, the stability conditions of the PFMB systems equipped with mismatched IT2 membership functions are investigated. Unlike the membership-function-independent (MFI) methods, the information and properties of IT2 membership functions are considered in the stability analysis and contained in the stability conditions in terms of sum-of-squares (SOS) based on the Lyapunov stability theory. Three methods, demonstrating their own merits, are proposed to conduct the stability analysis for the IT2 PFMB control systems and all of the methods can achieve feasible control results. All the three approaches are well explained, which offers the reader systematic ways to include the information of the membership functions into the analysis. In addition, all the approaches are compared and the pros and cons are presented to help the reader choose the most appropriate approach in the applications. In the second task presented in Chapter 4, the membership-functions-dependent (MFD) methods have been proceeded to the tracking control problems and the output feedback tracking issues of IT2 PFMB fuzzy control systems are investigated. The output-feedback IT2 polynomial fuzzy controller connected with the nonlinear plant in a closed loop drives the system states of the nonlinear plant to track those of the stable reference model. The system stability is investigated based on the Lyapunov stability theory under the SOS-based analysis approach and the SOSbased stability conditions are derived subject to a prescribed H1 performance. Like in the first work, the information of membership functions is also included in the analysis to facilitate the analysis and help improve the tracking performance in terms of H1 performance. Considering the implementation of the mentioned control schemes on digital computers, the sampled-data control systems are investigated as the last work in the thesis, which is presented in Chapter 5. In this task, the IT2 PFMB tracking control system is extended to the sampled-data based one. Through using the sampled output of both the control system and the reference system, an IT2 polynomial sampled-data based output feedback fuzzy controller can be designed to ful ll the tracking control task, the stability conditions can be obtained in terms of SOS and the tracking error is attenuated by the H1 performance index. As did in the previous two works, the information of the IT2 membership functions is used to relax the stability conditions and improve the tracking performance. The approaches proposed in the thesis to relax the stability conditions as well as to improve the tracking performance of the IT2 PFMB control systems are proved through the Lyapunov based stability theory. Meanwhile, simulation examples are provided to demonstrate and verify the theoretical analysis.

Робота виконана в Інституті прикладного системного аналізу Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського»
У дисертаційній роботі запропоновано методологію підтримки прийняття рішень, яка з використанням розробленого системного підходу дозволяє підвищити достовірність розв’язків в складних слабко структурованих системах на основі ієрархічних та мережевих моделей і включає нові та удосконалені методи: оцінювання і підвищення узгодженості матриць парних порівнянь загального виду залежно від властивостей цих матриць, розрахунку довірчих інтервалів для локальних ваг, розрахунку нечітких локальних ваг, гібридний метод розрахунку локальних та агрегованих ваг, метод комплексного оцінювання чутливості розв'язку та спосіб оцінювання реверсу рангів при використанні різних правил комбінування функцій довіри. Розроблено нові методики, засоби та система моделювання експертного оцінювання. Практичне значення одержаних результатів полягає у створенні інструментарію у вигляді системи підтримки прийняття рішень, який застосовано при розв'язанні практичних задач на замовлення міністерств і відомств України.
In the dissertation work, an important scientific and technical problem has been solved, which deals with development of mathematical and methodological support for increasing the reliability of solutions to decision analysis problems in complex weakly structured systems based on hierarchical and network models. The scientific novelty of the work is determined by the following theoretical and practical results obtained by author. Using proposed systematic approach, a new methodology of decision support is developed, which allows to increase the reliability of solutions of decision analysis problems in complex weakly structured systems on the basis of hierarchical and network models. This methodology includes the proposed and described below methods and techniques. A new method for evaluating and improving the consistency of expert judgements, which are given in a form of pairwise comparison matrix, is developed. Features of the method include an analysis of property of weak inconsistency, the presence of cycles in a pairwise comparison matrix and a search for the most inconsistent element of this matrix. The method can be applied to pairwise comparison matrices of various types, including multiplicative, additive, fuzzy and other. A Transitiv method for searching the most inconsistent elements of the matrix is proposed. A method of flows for finding the most inconsistent element of the matrix is improved by taking into account the input flow. The simulation shows that the developed Transitiv method and the method of flows are more efficient than existing methods. Usage of the proposed method of consistency evaluating and improving allows to obtain pairwise comparison matrices of acceptable quality for all elements of the model and these matrices can be used further to find local weights of model’s elements. A new method for calculating confidence intervals of local weights is developed, which, unlike others, takes into account the uncertainty of scale, expert's personal qualities such as optimism and pessimism, and does not require comparison of groups of elements with the frame. The method is based on notions of the Dempster-Schafer theory of evidence and results of computer simulation of expert's judgments. An uncertainty index of expert judgments is proposed, assuming that this uncertainty is caused by above factors. An improved method for calculating fuzzy local weights on basis of fuzzy pairwise comparison matrix is proposed, which differs from others in estimating and increasing the consistency of the matrix and taking into account properties of weak and strong order preservation on a set of calculated fuzzy weights. This method, unlike existing ones, makes it possible to determine the weak inconsistency of fuzzy matrix, to assess the acceptability of inconsistency level of fuzzy matrix for reliable local weights calculation, and to find the most inconsistent elements of the matrix using methods developed for crisp matrices. A hybrid method for calculating aggregated weights of hierarchical model elements with interdependent decision criteria has been improved, when input data for evaluation are fuzzy expert judgments. Improvement consists in using the developed more effective methods for assessment and increasing of crisp and fuzzy expert judgements consistency. A method for complex sensitivity analysis of results has been improved by taking into account sensitivity analysis of local rankings of model’s elements. In the developed method for estimating local sensitivity, intervals and indices of stability of pairwise comparison matrix elements are calculated, which retain the best decision alternative and all ranking of alternatives. Resulting stability intervals allow to find critical elements of the problem that require more careful analysis. A new technique for estimating the rank reversal is suggested, which can appear after applying combination rules of confidence functions for model’s elements. Using this technique, the Dempster, Yager, Zhang, Dubois and Prada and other combination rules were examined. Cases and features of rank reversals appearance in these rules were revealed. New techniques and tools for modeling a process of decision alternatives evaluation by an expert of high competence, expert-optimist and expert-pessimist while performing pairwise comparisons are developed. Using these techniques and tools, efficiency of proposed methods has been proved. A decision support system has been constructed on basis of proposed methods and techniques. This system has been used to solve several practical problems. Within the work with the Ministry of Education and Science of Ukraine, critical technologies of the Ukrainian energy industry were assessed, priorities of technologies were calculated and aggregated according to hierarchical model of criteria, and on their basis the most priority technologies for implementation were identified. In the course of research work together with the Institute of Space Research, directions of the expedient use of space information for remote sensing of the Earth for geoinformation systems were evaluated and the relative demand for the space information in the national economy of Ukraine was determined. On order of the Kyiv City State Administration, social problems of the Kyiv city were estimated in terms of benefits, costs, opportunities and risks, followed by selection of priority activities for implementation and evaluation of scenarios of the transport system development. Results of the dissertation work have been introduced into the educational process of the department "Mathematical methods of system analysis" of Institute for applied system analysis of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.
В диссертационной работе предложена методология поддержки принятия решений, которая с использованием разработанного системного подхода позволяет повысить достоверность решений в сложных слабо структурированных системах на основе иерархических и сетевых моделей и включает новые и усовершенствованные методы: оценки и повышения согласованности матриц парных сравнений общего вида в зависимости от свойств этих матриц, расчета доверительных интервалов для локальных весов, расчета нечетких локальных весов, гибридный метод расчета локальных и агрегированных весов, метод комплексной оценки чувствительности решения, а также способ оценки реверса рангов при использовании различных правил комбинирования функций доверия. Разработаны новые методики, средства и система моделирования экспертного оценивания. Практическое значение полученных результатов заключается в создании инструментария в виде системы поддержки принятия решений, который применен при решении практических задач по заказу министерств и ведомств Украины.

Робота виконана в Інституті прикладного системного аналізу Національного технічного університету України «Київський політехнічний інститут імені Ігоря Сікорського»
У дисертаційній роботі запропоновано методологію підтримки прийняття рішень, яка з використанням розробленого системного підходу дозволяє підвищити достовірність розв’язків в складних слабко структурованих системах на основі ієрархічних та мережевих моделей і включає нові та удосконалені методи: оцінювання і підвищення узгодженості матриць парних порівнянь загального виду залежно від властивостей цих матриць, розрахунку довірчих інтервалів для локальних ваг, розрахунку нечітких локальних ваг, гібридний метод розрахунку локальних та агрегованих ваг, метод комплексного оцінювання чутливості розв'язку та спосіб оцінювання реверсу рангів при використанні різних правил комбінування функцій довіри. Розроблено нові методики, засоби та система моделювання експертного оцінювання. Практичне значення одержаних результатів полягає у створенні інструментарію у вигляді системи підтримки прийняття рішень, який застосовано при розв'язанні практичних задач на замовлення міністерств і відомств України.

Entre 1990 et 1994, deux expériences de transfert de temps ont été menées avec les satellites de télévision directe TDF2 et Télécom-2A, entre 41aboratoires : le L. P. T. F. (Paris), le C. N. E. S. (Toulouse), l'O. C. A. (Grasse) et l'Observatoire de Besançon. Le principe de l'utilisation passive des signaux de télévision transmis par les satellites géostationnaires à des fins de transfert de temps (comparaîson des écarts de temps d'horloges atomiques distantes) est exposé, ainsi que la configuration matérielle dans laquelles les deux expériences ont été effectuées. Les principales sources d'incertitude sur ces transferts de temps sont dues à l'incertitude sur la position du satellite, aux perturbations de la propagation des signaux, et aux délais internes de chaque station. Tous ces phénomènes sont analysées et leur influence sur l'exactitude des résultats est chiffrée. L'influence du mouvement du satellite est ensuite étudiée en détail, et trois méthodes sont proposées pour en réduire les effets : la première est une méthode différentielle qui exploite certaines propriétés de l'orbite géostationnaire ; la deuxième méthode est basée sur une détermination explicite de la position du satellite effectuée préalablement au transfert de temps proprement dit. La troisième méthode met en oeuvre un filtrage numérique (filtre de Kalman) des données acquises entre les quatre stations de l'expérience, dans le but de restituer l'orbite du satellite. Dans les configurations les plus favorables des stations utilisées, l'exactitude des transferts de temps effectués peut une dizaine de nanosecondes, et des instabilités de fréquence peuvent être mesurées au niveau de 10 [puissance] -13 après moins de 24 heures d'intégration, et de 10 [puissance] -14 après moins de 10 jours
Between 1990 and 1994, two time transfer experiments have been set up wilh direct TV satellites TDF2 ànd Telecom-2A, implying four laboratories : the L. P. T. F. In Paris, the C. N. E. S. In Toulouse, the O. C. A. In Grasse and the Observatory of Besançon. The principle of time transfer (time comparison or remote atomic clocks, by passive use of television signals broadcasted by geostationary satellites is described together with the experimental setup that was used. The main sources of uncertainty on the time transfer are the uncertainty on the satellite position, perturbation of the signal propagation. And internal delays. All these phenomena are studied and their influence on the accuracy of the results is evaluated. Influence of the satellite motion is studied in detail, and three methodes are proposed to lessen its influence : the first one takes advantage of some properties of the geostationary orbit ; the second method is based on an explicit detemination of the satellite position carried out before the time transfer itself. The third method is a numeric (Kalman) filter using data from 4 stations in order to perform orbit restitution. Ln most favorable configurations, accuracy of time transfer can reach about 10 ns, and frequency instabilities lower han 10 [to the minus] 13 can be measured after an averaging tune of one day, or lower than 10 [to the minus] 14 after less than 10 days

Cette thèse fait partie d'un travail collaboratif avec des partenaires industriels et universitaires. Ses 2 principaux résultats sont : - La modélisation en 3D d'une vendangeuse qui est un exemple typique de véhicule tout-terrain reconfigurable. Le contexte de l'environnement 'tout-terrain' a focalisé cette étude sur un modèle d'interaction pneumatique/sol qui prenne en compte les inégalités et les déformations du terrain. En particulier, on tient compte du fait que chaque contact roue/sol n'est pas ponctuel et qu'a fortiori, les 4 zones de contacts ne sont pas coplanaires. Un calcul ensembliste des zones de contact est fait en utilisant une version de l'algorithme SIVIA adaptée à MATLAB. Le résultat pour chaque zone de contact est un sous pavage ou une boite englobante selon la précision et la rapidité de calcul souhaitée. On dispose ainsi d'un ensemble de polygones de sustentation pour faire un diagnostic de non renversement du véhicule. - La définition de 2 indicateurs du risque de renversement sont ensuite proposés. L'un d'eux se base sur le concept de "Zero Moment Point (ZMP)" en calculant une distance de la position du ZMP par rapport aux 4 côtés de l'ensemble des polygones de sustentation. L'autre critère de tendance au renversement calcule la vitesse de rotation du véhicule par rapport à un ensemble d'axes de renversement. La prédiction du risque de renversement est proposée sous la forme de la prédiction de la position du ZMP ou du critère "Time to Rollover". Chacune de ces méthodes ont été évaluées avec des données expérimentales réelles et simulées. La suite de ce travail est une mise en commun de ces résultats avec d'autres méthodes proposées par nos partenaires.

This PhD thesis treats some problems concerning nonlinear differential equations. In the first two papers computer-assisted proofs are used. The differential equations there are rewritten as fixed point problems, and the existence of solutions are proved. The problem in the first paper is one-dimensional; with one boundary condition given by an integral. The problem in the second paper is three-dimensional, and Dirichlet boundary conditions are used. Both problems have their origins in fluid dynamics. Paper III describes an inverse problem for the heat equation. Given the solution, a solution dependent diffusion coefficient is estimated by intervals at a finite set of points. The method includes the construction of set-valued level curves and two-dimensional splines. In paper IV we prove that there exists a unique, globally attracting fixed point for a differential equation system. The differential equation system arises as the number of peers in a peer-to-peer network, which is described by a suitably scaled Markov chain, goes to infinity. In the proof linearization and Dulac's criterion are used.

Cette étude porte sur l'implantation de l'algorithme FxLMS pour la réduction du bruit généré par un ventilateur en conduit. Les variations de régime du ventilateur génèrent des instabilités de l'algorithme lors d'un contrôle des modes (0,0) et (1,0) avec un échantillonnage synchrone. Une théorie permet de prévoir les intervalles de fréquence d'échantillonnage garantissant la stabilité. Une validation expérimentale a été réalisée et elle a montré que les intervalles théoriques approchaient l'expérimentation avec des erreurs d'environ 10%. Les stratégies de contrôle modal et couplé ont été employées en temps réel grâce à une identification tonale permettant une comparaison expérimentale. Les résultats obtenus sont sensiblement équivalents avec des atténuations de 14 dB. Le contrôle modal est plus sensible à l'effet de "spillover" avec une éventuelle détection du mode (0,1). Le contrôle couplé nécessite plus de ressources système mais offre une qualité de contrôle optimale
This study is based on FxLMS algorithm implementations for control of noise produced by axial air-fan. Instabilities have appeared because of this primary source variations during modal control of (0,0) and (1,0) modes. Theoretical studies have been done and it is possible to foresee sampling frequency stability intervals. These intervals approach experimental results with 10% errors. Tonal identification, because of lower computation time needs, has allowed Independant Modal and Fully Coupled Controls in real time which have been compared. These two strategies have given equivalent reductions around 14 dB. Results confirm simulations done in previous studies. It has ben shown that modal control is more sensitive to spillover effect maybe because of (0,1) mode disturbations. Coupled control needs more computation power but gives better control quality

Cette thèse traite de méthodologie pour l'analyse et la commande de systèmes linéaires à retards. On s'intéresse plus particulièrement à trois techniques complémentaires. La première est l'approche géométrique. Les systèmes linéaires à retards peuvent se modéliser par un quadruplet de matrices à coefficients sur un anneau. L'approche géométrique consiste alors à étudier un système avec les propriétés des modules de cet anneau. Dans cette partie, on développe une analyse exhaustive des notions d'invariance de modules, en vue d'applications en commande. Des relations logiques entre différentes formes d'invariance contrôlée et d'invariance conditionnelle sont établies. La deuxième approche étudiée dans cette thèse est algébrique. Pour celle-ci, l'utilisation de pseudo-polynômes, qui sont des opérateurs faisant appel à un nombre fini de dérivateurs, de retards ponctuels et distribués, se révèle fondamentale. On utilise plus précisèment l'anneau des fractions propres et stables de pseudo-polynômes pour résoudre le problème de stabilisation d'un système. Ce problème débouche sur une paramétrisation des compensateurs stabilisants et des matrices de transfert en boucle fermée. On étudie alors divers problèmes de commande, comme le rejet de perturbation, l'atténuation de perturbation, la poursuite de modèle exacte ou approchée, ou la commande optimale au sens L1. Enfin, la troisième et dernière approche est le calcul numérique. Dans cette partie, on utilise le calcul par intervalles pour résoudre des problèmes numériques difficiles, comme la stabilité robuste, la stabilisation, ou encore le respect d'un gabarit de performances et de robustesse.

碩士
國立中興大學
水土保持學系
90
The major purpose of this study is to discuss the influence that ground sills are established in riverbed. In addition, it conducts clear-water discharge flume experiments that can know the sand volumetric movement changes in different protection ranges of ground sills and the efficiency to stabilize the channel-bed. The result of the study infers that channel-bed scour has gone down with the decrease of the interval ground sills, this shows ground sills has the ability to stabilize the channel-bed. Besides, the influence of ground sills is lead channel-bed scour to pass through protection ranges of ground sills and make carry soils amount of water constant, not control the scour by gnawing water power. Another, we know the data intense increase and are close to extreme value when interval of ground sills are 2~7 times channel wide. Besides, the effect of full river length protection to steady channel and reduce scour rate is better than half section protection. By the relationship between average scour rate of riverbed and stream power,we know that have direct proportion between them. According to this, under the protection range of ground sills are based on known terms like components of the interval ground sills, we establish the relationship equation among average scour rate, stream power, critical silt start power, interval of ground sills and slope gradient: the related coefficient r2=0.89.We can figure out average scour rate of riverbed by interval ground sills have been known, and hope to provide for the field operation further.

博士
國立中央大學
數學系
85
This thesis gives a study of an aspect of asymptotic stability theory of matrices. Using the notions of the asymptotic stability (in the sense of Lyapunov), we prove an asymptotic stability theorem for matrices. By making use of this stability theorem, we give a new proof of the recent conjecture byDaubechies-Lagarias (1992). By inducing the notion of majorant, we give a characterization of the simultaneous Schur stability for a familily ofinterval matrices. From this characterization, an inequality for spectral radii is obtained. As an application of this inequality, we introduce efficientconditions for the stability of linear interval systems.

Thesis (Ph. D.)--University of Notre Dame, 2005.
Thesis directed by Mark A. Stadtherr for the Department of Chemical and Biomolecular Engineering. "July 2005." Includes bibliographical references (leaves 113-120).

William C. Karl, George C. Verghese.
Caption title.
Includes bibliographical references (leaves 17-18).
Partiially supported by the U.S. Army Research Office, Center for Intelligent Control Systems. DAAL03-86-K-0171

碩士
逢甲大學
土木及水利工程研究所
88
The major purpose of this study is to discuss the influence that consolidation works are established in channel-bed. On the other hand, it conducts clear-water discharge flume experiments that can know the sand volumetric movement changes in different protection ranges of consolidation works and the efficiency to stabilize the channel-bed. The result of the study infers that channel-bed scour has gone down with the decrease of the interval consolidation works, this shows consolidation works has the ability to stabilize the channel-bed. Besides, further discussions are made among sand transportation in some downstream area, where channel-bed is under protection by consolidation works and with the Japanese’s research or this study result data, we know that mass erosion are form downstream when consolidation works are established. In addition, in parts of river channel, downstream erosion will reduce when consolidation work interval decreases; this proves that when consolidation works are set in parts of area, it has certain degree of efficiency in downstream bed erosion. With consideration of the affection in bed load transmission after setting consolidation works, and apply the relationship between the rate of channel-bed scour and stream power, we find out the rate of channel-bed scour has the direct proportion with the stream power and the critical stream power for initiation of sediment has 1.5 square direct proportion with the representative diameter of sediment. According to this, under the protection range of consolidation works are based on known terms like components of the rate of channel-bed scour, stream power and slope gradient, we establish the design model that the interval of consolidation works and embankment height and hope to provide for the field operation further.

碩士
國立中正大學
光機電整合工程研究所
102
In this thesis, an interval Type-2 Takagi-Sugeno fuzzy logic control system (IT2 T-S FLCS) with model uncertainty and external disturbance was investigated; the control systems consisted of an IT2 T-S fuzzy model and IT2 fuzzy controllers. The IT2 T-S fuzzy model has greater capability to simulate a plant, compared with the traditional T-S fuzzy model. This thesis presents new theorems that can be used to design IT2 fuzzy controllers, and it demonstrates that a nonlinear system with model uncertainty and external disturbance can be globally asymptotically stabilized using these controllers. Four linear matrix inequality based (LMI-based) stability conditions for the IT2 T-S FLCS are presented. LMI-based robust stability conditions are inferred from the Lyapunov function, which can be numerically solved using the Matlab LMI Toolbox. The results of simulations are provided to illustrate the following: First, fuzzy controllers designed using the proposed theorems have greater capability to deal with model uncertainties. Second, the stability conditions proposed are more general and relaxed compared with existing LMI-based approaches. Finally, the feasible area is greater compared with that in the traditional LMI-based approach.

碩士
國立臺北科技大學
電機工程系研究所
100
In this thesis, the delay-range-dependent stability of linear systems with interval time-varying delay will be studied. It is mainly based on Lyapunov-Krasovskii methodology. The derivation techniques include the delay free weighting matrix (FWM) method, Jensen''s integral inequality, the convex combination technique, and the linear matrix inequality (LMI). Stability criteria are given in terms of LMIs, and numerical examples are given to illustrate the effectiveness and the merits of the results. To this end, we first decompose the lower bound delay interval into multiple equidistant subintervals, then construct augmented Lyapunov functionals which contains some triple-integral terms on these intervals and the time-varying delay interval. Consequently, a novel augmented Lyapunov functional is proposed. Secondly, by using FWM approach, Jensen''s integral inequality and the convex combination technique, some new stability criteria for interval time-varying delay systems are derived in terms of LMIs. Finally, numerical examples are presented to demonstrate the less conservatism of the obtained results, when compared to existing results.

博士
中原大學
電機工程研究所
103
Real-time network control applications have gained great attentions owing to the rapid development of data communication network technologies. However, networked control system (NCS) also result in unavoidable problems in time delays that seriously degrade control performance and stability. The characteristics of network-induced delays may be in constant, bounded, random, or unpredictable natures depending on the network protocols, nodes, software, and hardware. Moreover, the existence of time-delay is frequently a source of instability in the real systems. Therefore, the problem of stability analysis of time delay nonlinear systems with a dead zone has been one of the most important topics for the control design engineer. We propose improved stability criteria for linear systems with interval time-varying delay using a novel partitioning technique. Here, we choose an appropriate Lyapunov-Krasovskii functional, where free weighting matrices, completion of squares method and zero equalities are applied to obtain the stability criteria. Especially, the new technique is to partition the integration into as many intervals as possible to obtain the relaxed criteria. On the other hand, we present an linear matrix inequality (LMI)-based approach to stabilize networked converters with nonlinear dynamics. The system consists of a common controller remotely regulating converter outputs where the network induces time-varying delay. The research problem is to derive the theoretical bound of time delay which is a practical consideration for networked converter applications. We first represent the networked converter into a Takagi-Sugeno (T-S) fuzzy system. Then using a carefully chosen Lyapunov-Krasovskii functional approach, we derive the sufficient conditions of stabilization of the T-S fuzzy system. We transform the sufficient conditions into LMIs. By solving the LMIs numerically, we obtain the controller gains and the maximum allowable upper bound (MAUB) of time delay. Compared to conservative results using typical Lyapunov-Krasovskii functional approaches, the MAUB obtained here is quite practical for the networked converters. We then carry out numerical simulations and practical experiments where satisfactory results further verify the theoretical derivation.

碩士
國立中央大學
電機工程學系
106
This thesis is concerned with stability analysis and controller design of interval positive systems with delay. The research scope is discrete-time systems. The interval and delay time contained in the system are the factors of uncertainty. For the problems of positiveness and stability analysis, we derive some new sufficient and necessary conditions. Based on these conditions, the design of the controllers with the state feedback can be applied to the stabilization design of the control system. Using the results of the foregoing analysis, the parameters of the controllers are sought in conjunction with the linear programming method. Finally, taking the actual discrete-time interval positive system with delay as an example. The simulation results,show that the designed controllers are effective and applicable.

碩士
國立臺灣海洋大學
通訊與導航工程學系
102
The target of this thesis is to establish new robust stochastic stability criteria of Markovian delayed genetic regulatory networks with interval parameters. The Markovian stochastic delayed genetic regulatory networks can be analyzed by applying stochastic differential equation theory and Markovian jumping parameters. The SUM regulatory functions are applied to model the genetic regulatory mechanism and the Markov chain process is utilized to represent the state switching mechanism of hybrid genetic regulatory networks. In addition, due to chemical reactions, modeling errors and measurement accuracy, the negative effects of time-varying delays and interval parameters in genetic regulatory networks should be overcome. Moreover, the robust stability of Markovian stochastic delayed genetic regulatory networks subjoined with the biological noises such as impulse, Brownian motion and Poisson jump is investigated also. Inequality bounding techniques and free-weighting matrices are employed to derive Lyapunov functional based sufficient conditions for the robust asymptotic stability. The less conservatism of the asymptotic stability criterion can be reduced by utilizing Jensen’s integral formula and distribution parameters. In the real world, the organism has a finite lifecycle. The method for achieving finite-time or short-time stability such that the transient state performance can be guaranteed is worth developing. All proposed asymptotic stability conditions can be easily transferred to linear matrix inequality (LMIs) by Schur complements. Furthermore, the exponential stability in mean square for Markovian stochastic delayed genetic regulatory networks with Poisson jumps is addressed and the sufficient delay-dependent conditions are obtained by employing Gronwall-Bellman inequality, semigroup theory, and Holder inequality. On the other hand, sufficient time-independent conditions of the exponential stability in pth moment for Markovian stochastic delayed genetic regulatory networks is researched by using fixed point theory and contraction mapping principle. Finally, some numerical examples are presented to demonstrate the effectiveness of the developed results.

碩士
國立中正大學
光機電整合工程研究所
101
In this thesis, we introduce the stability conditions for continuous and discrete time systems with time-delay based on interval type-2 fuzzy T-S logic control systems (IT2 T-S FLCSs). Since, T-S fuzzy models can represent complex nonlinear systems with fuzzy sets. An interval type-2 fuzzy set (IT2 FS) provides additional degrees of design freedom, which enhances model uncertainty and parameter perturbation capabilities. We therefore combine an IT2 FS with T-S fuzzy model to design a controller for an IT2 T-S FLCSs. The proposed stability conditions are formulated in the form of linear matrix inequalities LMI, which can be solved easily using software such as the Matlab LMI toolbox. Finally, we demonstrate the performance and stability of an IT2 T-S FLCSs with time-delay by showing the simulated results.

碩士
國立彰化師範大學
工業教育與技術學系
97
This thesis presents the complete study of stability analysis and state estimator design. The system is focused on discrete stochastic recurrent neural networks with interval time-varying delays. For a stability analysis problem, the goal is to develop globally robust delay-dependent stability for uncertain discrete stochastic recurrent neural networks with interval time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded in the neuron state and activation functions. The activation functions are assumed to be globally Lipschitz continuous. Based on the Lyapunov-Krasovskii functions combining with linear matrix inequality (LMI) techniques, globally robust delay-dependent stability criterion which is dependent on both the lower and upper bounds of the interval time-varying delays is derived by introducing some free weighting matrices. For the estimator design problem, state estimation for discrete stochastic recurrent neural network with interval time varying delays was investigated. Attention was focused on the design of a state estimator which ensures the global stability of the estimation error dynamics. A delay-dependent condition on both the lower and upper bounds of the interval time varying delays is given in terms of a linear matrix inequality to solve the neuron state estimation problem. When this LMI is feasible, the expression of a desired state estimator is also presented. Finally, some numerical examples are provided to demonstrate the applicability of the proposed approach.

碩士
國立高雄海洋科技大學
輪機工程研究所
102
In this dissertation, the switching signal design of uncertain discrete switched systems with interval time-varying delay and linear fractional perturbations is investigated. Some linear matrix inequality (LMI) criteria are provided to design the switching signals which guarantee the stability of discrete switched time-delay system. Some nonnegative inequalities and delay-partitioning approach are introduced to improve the conservativeness of the proposed results. Finally, some numerical examples are illustrated in respective chapter to show the main proposed results.

碩士
國立彰化師範大學
工業教育與技術學系
100
This thesis presents the complete study the robust stability problem for uncertain discrete-time genetic regulatory networks with disturbance attenuation and infinite-distributed interval time-varying delays. The time-varying delays are assumed to be with both upper bound and lower bound in the discrete-time domain, and the uncertain parameters are norm-bounded. By using a Lyapunov-Krasovskii functional method and linear matrix inequality (LMI) techniques with the combination of the Hybrid Taguchi-genetic algorithm (HTGA), we can tackle the disturbance attenuation H-infinity stability problem such that with the specified performance is minimized for the system under disturbance attenuation. For the infinite-distributed time-varying delays problem, a sufficient condition is established that guarantees the robust stability for discrete-time uncertain genetic regulatory networks with infinite-distributed delays. An important feature of the results lies in that the robust stability conditions are dependent on the lower and upper bounds of the delays, which are made possible by using improved bounding to the technique to reduce the conservatism of the criterion due free weighting matrices are induced. Finally, some illustrative examples are provided in order to illustrate the applicability and effectiveness of the proposed theoretical results.

Malignant ventricular arrhythmias are a common cause of sudden cardiac death. Moderate therapeutic hypothermia (MTH) is routinely used in post-resuscitation care for anticipated neuroprotective effects. However, the safety of MTH in terms of the electrical stability of the heart has not been satisfactorily proved yet. Also, the increased sympathetic tone in patients with heart failure contributes to a higher incidence of malignant ventricular arrhythmias. The aim of this work was to verify the safety of MTH as regards the inducibility of ventricular fibrillation (VF) in the pig biomodel, especially in relation to spontaneous changes in the kalemia and QT interval. Furthermore, we assumed that renal denervation (RDN) could reduce the inducibility of VF. In the first part of the thesis, the extracorporeal cooling was introduced in fully anesthetized swine (n = 6) to provide MTH. Inducibility of VF was studied by programmed ventricular stimulation (8 basic stimuli with up to 4 extrastimuli) three times in each biomodel under the following conditions: during normothermia (NT), after reaching the core temperature 32 řC (HT) and after another 60 minutes of stable hypothermia (HT60). VF inducibility, effective ventricular refractory period (ERP), QTc interval, and potassium plasma level were measured. In...