Guaranteed Cost Control For Uncertain Time-delay Systems

In terms of the Lyapunov technique,concept of generalized quadratic stability,linear matrix inequalities (LMI) and theory of guaranteed cost control, the problem of guaranteed cost control for uncertain time-delay systems are studied in this dissertation. Aimed at the uncertain singular time-delay systems possessing norm-bounded parameter uncertainties , this dissertation studies delay-dependent dynamic state feedback guaranteed cost control problem of the systems chiefly, it obtain a delay-dependent sufficient condition for the existence of the guaranteed cost controller. Then, this dissertation studies the problem of guaranteed cost control for uncertain discrete time-delay systems .The main contents consist of several parts as follows.1. A survey of guaranteed cost control for dynamic systems is presented. The main results in classic guaranteed cost control are firstly introduced. Then, emphasis is put on the situation of guaranteed cost control in recent years. Some typical application problems of guaranteed cost control are discussed and some open questions are pointed out. Finally, present the content arrangement of this dissertation.2. This section considers the problem of dynamic state feedback guaranteed cost controller design for time-delay systems possessing norm-bounded parameter uncertainties. Firstly, a delay-dependent stability criterion for the normal singular time-delay system is established, which guarantees the system to be regular, impulse free and asymptotically stable. Then, based on the concept of generalized quadratic stability, a delay-dependent sufficient condition for the existence of the guaranteed cost controller is obtained.3. This section firstly deals with the guaranteed cost control problem for a class of discrete linear systems with norm-bounded uncertainties and multiple state delays, together with a given quadratic performance index. A sufficient condition is presented for the existence of memoryless state feedback guaranteed cost control laws and a parameterized representation of the guaranteed cost control laws is given in terms of the feasible solutions to a certain linear matrix inequality.