Exponential Stability Analysis For Some Classes Of Switched Systems With Delay

In modern control theory, the switched systems is an important class of hybrid dynamic systems. Because a lot of time delay exists in the network control systems, mechanical transmission, metallurgical industry and bio-engineering and other types of systems, studying the stability of switched system with delay is particularly important. Composition of the switched systems are different from the general systems. It consists of several subsystems and switching rules. The switching rules of these subsystems can directly affect the stability of the entire system.This thesis mainly studies exponential stability of time-varying switched systems with time delay. The appropriate Lyapunov-Krasovskii functional is selected by using the Lyapunov stability theory. And the sufficient condition of exponential stability can be obtained by the method of average dwell time and LMI. When the average dwell time of switched systems is long enough in each stable subsystems, the exponential stability of the entire system can be guaranteed. The research results can be divided into two parts as following:On the one hand, The exponential stability of two kinds of time delay switched systems are studied mainly. They are time-varying switched systems with time delay and the system with two nonlinear perturbations. By choosing a more complex Lyapunov-Krasovskii functional, using the integral inequality, the criteria that can guarantee system stability are gotten through constructing appropriate free weighting matrices. On the other hand, by introducing appropriate free weighting matrices, the exponential stability of neutral switched systems with time delay is studied with the method of average dwell time and LMI. The neutral switched systems with time delay include neutral time-varying switched systems with time delay and the system with two nonlinear perturbations.In addition, in the last part of each chapter, through numerical examples demonstrate the effectiveness. In addition, in the last part of each chapter, the validity of the results is verified through numerical examples.