Study On Stability And Robust Control For Discrete Impulsive Switched System

Switchings and impulses occur frequently in many fields of modern science such as computer science, robotics, communication, economy, and automotive industry. However, there are some limitations in modeling and analyzing the real world problems by pure switched systems or pure impulsive systems. Consequently, the area of impulsive switched systems has attracted wide attention of many researchers.Time delay is often the root of poor performance and instability of the system. Moreover, uncertainties may also badly influence the control performance and control requirements of the system. Therefore, study on impulsive switched systems with time delay and uncertainty has become absolutely necessary. But the known results in existing literature are all delay-independent conditions for Lyapunov stability, robustness and H_∞control of the impulsive switched systems. Delay-dependent research results have not been found in the published literature. On the other hand, most of the theoretical results on impulsive switched systems are for the continuous systems and very few results on discrete impulsive switched systems are available in the existing literatures.The objective of this dissertation is to deal with the problems of robust stability, H_∞control and guaranteed cost control of discrete impulsive switched systems with norm-bounded parameter uncertainty and time invariant delays. By using Lyapunov-Krasovskii functional approach, multi-Lyapunov functional method and linear matrix inequality (LMI) techniques, some sufficient conditions are established in discrete domain. To reduce conservativeness, some delay-dependent conditions are derived by considering the influence of time delay for the system stability and performance index after some delay- independent criteria are obtained.Chapter 1 surveys the history and development of switched systems and impulsive systems. The basic theory and research results of H_∞optimal control and guaranteed cost control are introduced as well. The main contents and results of the dissertation are given as follows.In Chapter 2, stability analysis and stabilization problems are investigated for discrete impulsive switched systems with uncertainty and time delay. Some delay-dependent criteria and delay-independent criteria on asymptotic stability are derived, respectively. The sufficient conditions are equivalent to an LMI solvability problem by matrix transformation. A stabilization condition using a feedback controller is formulated to stabilize the closed-loop system.Guaranteed cost control problems of a discrete impulsive switched system with parameter uncertainty and time delays are investigates in Chapter 3. A new quadratic cost index is introduced for the given system. Some delay-dependent conditions and delay-independent conditions for the existence of guaranteed cost state feedback controller are derived, respectively. We also conclude that these conditions are equivalent to some LMI solvability problems and the feasible solutions provide a parameterized representation of guaranteed cost controller and performance bound.Chapter 4 studies the robust H_∞control for a discrete impulsive switched system with parameter uncertainty and time delays. Some sufficient conditions for existence of robust H_∞stability with robust performance y are derived in discrete domain for impulsive switched systems. Then the parameterized representation of state feedback controller is obtained based on the LMI techniques. Some delay-dependent criteria and delay-independent criteria for robust H_∞control are derived in the form of LMI, respectively.Finally, a conclusion of the dissertation and some future research topics in the field are given in Chapter 5.