Stabilization Of Switched Systems With Time Delay

In this paper,the stabilization problem of the switched systems with time delay is studied.For the controllable switched systems with time delay,first,feedback laws and switching laws are designed to stabilize the systems,then the exponential stability of the systems is discussed by the estimation of the closed-loop systems' trajectory.From the point of switching frequency view,the switching law is constructed in the paper.If the upper bound of the switching frequency which the switching law constructed is small enough,as a result the exponential stablity is got.From the remark of theorem 3.3,if the switching frenquency f=1/τ,that is,α＞1/τ,the switching law can be chosen arbitrarily. So that in the application,it is not necessary to design the swiching law specially. The result is perfect that just required the design of the state feedback laws.