Input-to-state stability for nonlinear systems with large delay period based on switching techniques

The paper is concerned with the problem of input-to-state stability (ISS) for a class of systems with large delay period (LDP). The concepts of the length rate of LDP and the frequency of LDP are introduced. First the considered system is converted into a switched delay system which may include an unstable subsystem. Then based on a piecewise Lyapunov functional, the ISS conditions of the systems are developed under the constriction of length rate and the frequency of LDP.