Robust Stability Analysis And Guaranteed Cost Control For Time-Delay Switched Systems

Switched time-delay systems are a kind of switched systems with time-delay. Their dynamics become very complex because of the interaction among their continuous dynamic, discrete dynamic and time-delay. The stability of switched time-delay systems is divided into delay-independent stability and delay-dependent stability. By using the common Lyapunov function method, multiple Lyapunov function method, LMI method, etc., the problems of quadratic stability, delay-independent stability, delay-dependent stability and robust guaranteed cost control for uncertain switched systems are studied. The main results are summarized as follows:First, quadratic stability of a class of uncertain switched time-delay systems is studied. There are bounded norm uncertainties in systems matrix, time-delay matrix and input matrix and outside disturbances for every subsystem. By using completeness condition, multiple Lyapunov function and LMI methods, two sufficient conditions of quadratic stability are given and two kinds of switching laws are designed for uncertain switched time-delay systems. The stable conditions can be changed into the feasible solution for a set of matrices inequalities. The simulation shows the validity of the results.Then, the guaranteed cost control problem for a class of switched time-delay with uncertain parameters is considered. The memoryless state-feedback controllers which can make the states of the closed loop systems asymptotically stable are designed. The sufficient condition of robust guaranteed cost for switched systems existing common Lyapunov function with arbitrary switching is given, and the sufficient condition of robust guaranteed cost for switched systems which do not exist common Lyapunov function is also given, by multiple Lyapunov functions method designing switching law. The results can be solved by LMI. The simulation shows the validity of the results.Last, the delay dependent robust stability for a kind of uncertain switched time-delay systems is investigated. By multiple Lyapunov functions methods and LMI method, under the assumption which every subsystem can not be stabilizable, the sufficient condition of time-dependent asymptotical stability for uncertain switched systems with state-feedback is obtained. The switching law is also designed.