Stability Research For Switched Delay Systems

In the natural world and society practice, many objective things' development depend on past behavior or state. This kind of property is called time delay. Time delay is often the reason of instability and chaos. In recent years, many researchers have devoted to study the relevant control problems of time-delay systems. In addition, in recent years, due to the vast application of switched system control, there is an increasing interest on the modeling, analysis, synthesis, and control of switched systems. Nowadays more and more people have paid attention to the stability analysis of the switched systems and the study of the switching control. Mechanism of system evolution is not clear and many problems of analysis and syntheses need to be studied. This dissertation studies stability of switched delay systems and the main contributions are as follows.An average dwell time method is introduced into non-linear switched delay systems. Conditions in the form of linear matrix inequalities (LMIs) are presented to guarantee robust exponential stability of such systems with exponential decay estimates for the states explicitly developed.The problems of exponential stability and L2-gain for one type of switched delay systems with time-varying delay are studied by using average dwell time method. A class of switching signals are given such that the considered switched delay systems are exponentially stable and have weighted L2-gain. Sufficient conditions in the form of LMIs are given to guarantee the existence for such switching signals. Moreover, state decay estimates are also presented.Asymptotical stability of non-linear switched neutral delay systems is considered. Based on single-Lyapunov function technique and multiple-Lyapunov function technique, some sufficient conditions of asymptotical stability and the corresponding switching laws are given in the form of LMIs.The problem of hybrid state feedback guaranteed cost control with optimization design is discussed for a class of uncertain non-linear delay systems. When there exist finite candidate controllers with known controller gain matrices and none of the controllers can solve the problem based on single-Lyapunov function method, control laws for the existence of hybrid state feedback guaranteed cost controllers are given, so that the system satisfies hybrid state feedback guaranteed cost controllers. In the case of unknown controller gain matrices, by means of multiple function technique, similar conditions, and design method for controller gain matrices are also given. Moreover, an optimization scheme of computing a cost upper bound is given.At the same time, some corresponding numerical examples are given to show the correctness and validity of conclusions.