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Passivity Of Singular Systems And Synchronization Analysis Of Chaotic Systems

Posted on:2011-02-13Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y B GaoFull Text:PDF
GTID:1118360305499215Subject:Operational Research and Cybernetics
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The passivity of singular nonlinear systems and the synchronization analysis of chaotic systems are very important research fields in the complex system control theory. Due to the complexity of the nonlinear system, the research on the passivity of singu-lar systems and the synchronization analysis of chaotic systems is now in a developing stage, development of passive control for singular systems and of chaos synchronization are of two important research contents in the control theory. At present, there are many problems to be solved, such as the passive control for the singular nonlinear systems, the passivity analysis of nonlinear singularly perturbed systems, the dissipative master-slave synchronization of chaotic systems, the impulsive synchronization of discrete-time chaotic systems, the dynamic output feedback controller design for drive-response synchroniza-tion of chaotic systems, and so on. The major contributions of this dissertation are as follows.(1) The passive control problems are studied for the continuous singular systems with nonlinear perturbations. By using the Banach Fix-Point Principle, Picard-Lindelof Theorem and the Lyapunov approach, the passivity condition, the condition for the existence-uniqueness of solution and exponential stability condition are derived for this class of systems, and the unified formula which includes these sufficient conditions is firstly expressed in terms of linear matrix inequalities, then the state-feedback controller based on passivity is designed.(2) The passivity analysis problems are addressed for the uncertain singularly perturbed systems. Based on Lyapunov stability theory and a singular system approach, the Klimushchev-Krasovskii Lemma is firstly formulated in terms of linear matrix inequalities, and some sufficient conditions of asymptotic stability and passivity for this class of systems are given, then the maximum stability bound for the uncertain singularly perturbed systems can be obtained via solving the generalized eigenvalue problem.(3) The dissipative master-slave synchronization problems are investigated for chaotic systems under information constraints. By using sampled-data method, Lyapunov-Krasovskii approach and free weighting matrix technique, in which the transmission-induced time delay, data packet dropout and measurement quantization have been taken into consideration, the dissipative synchronization criterion for the master-slave synchronization of chaotic systems is firstly derived in the form of a linear ma-trix inequality, and the dissipative quantized state-feedback controller is designed.(4) The impulsive synchronization problems are considered for the discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered, sufficient conditions for asymptotic stability of synchronization er-ror systems are firstly given in terms of linear matrix inequalities and algebraic inequalities.(5) The drive-response synchronization problems are discussed for chaotic systems via time-varying dynamic output feedback controller. Based on the Lyapunov-Krasovskii approach, a novel synchronization criterion is firstly obtained and formulated in the form of a linear matrix inequality, and a sufficient condition on the existence of a time-varying dynamic output feedback controller is derived.
Keywords/Search Tags:Singular systems, singularly perturbed systems, chaotic systems, linear matrix inequalities, asymptotic stability, passivity, passive control, state feedback, dynamic output feedback, time-varying delay, quantization, information constraints
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