New Theorem for Asymptotically Stability of Time-Delayed Systems

This paper deals with the problem of the asymptotical stability for a class of linear systems with multiple time-delays. Using Lyapunov-Razumikhin theorem and the concept of matrix norm, the sufficient conditions of delay-independent stability and delay-dependent stability are derived to ensure that the linear systems with multiple time-delays are asymptotically stable. By comparing with the present theorem, it is obvious that the stability theorem in this paper could deal with the linear systems with constant delay and time-varying delay. Last, an example is given to illustrate that the new method is more effective than the present method and the delay bound obtained in this paper is of less conservative.