Research On Robust Stability, Robust Control And Impulsive Stabilization For Impulsive Delay Systems

It is more general and complex than that of classical delay systems and ordinary differential systems for impulsive delay systems. Its robust stability and control performance may change for impulsive effects, so the studies on impulsive delay systems have important theoretical meaning and practical values, which have been widely considered by many researchers.The research of this paper is supported by NSFC Key Project (60334010), NSFC(60474047), SRFDP(2003056103) and Guangdong Province Nature Foundation of China Project(31406). With Linear Matrix Inequality approach, this dissertation focuses on robust stability, robust H_∞ control and robust guaranteed cost control onlinear impulsive delay systems, stability on impulsive delay Lurie systems, and impulsive control and stabilization for time-invariant and time-variant delay systems. So the theory of impulsive delay control systems is established. The impulsive effects are considered as both perturbation factors and control factors. The main work of this paper is as follows:1. It discusses the stability for linear uncertain impulsive multi-delay systems with scalar-bounded and norm-bounded uncertainties, some sufficient criteria on robust asymptotic stability are established. Based on LMI approach, its stability can be analyzed to solve corresponding LMIs. The influence of not only time delays on stability is considered, which the delay-dependent and delay-independent criteria are presented, but also impulsive effects are considered, which the systems are asymptotical stable for impulsive effects.2. The robust control problems on impulsive delay systems are studied. First, it discusses the H_∞ robust control for impulsive multi-delay systems with scalar-bounded and norm-bounded uncertainties. Some sufficient criteria are established which the closed-loop systems satisfy robust stability and H_∞ performance with LMI approach, the design of corresponding H_∞ controller is given. Second, robust guaranteed cost control for these systems is discussed. Some sufficient criteria are established which the closed-loop systems satisfy robust stability and square performance, the corresponding controller is also obtained.3. It discussed the absolute stability problems on impulsive delay Lurie systems,...