The Stability Analysis For A Class Of Switched System

In the first part of the paper,we mainly discuss the stability of a class of subsystem that is linear time-varying normal switched system. If the given assumption is satisfied,we can find out a common quadratic Lyapunov function for all the subsystems.So the switched systems are exponentially stable under the arbitrary switching law. In addition,there is polytopic combination among the time-varing subsystems of the switched system that the given assumption is not satisfied,we design a switching law connected with time and state,and guarantee the asympotical stability of systems.In the second part of this paper,we study the periodic stabilization of linear switched system.A sufficient condition of the switching law which makes the state exponential convergence is presented.