Input-to-State Stability Of Time Delay Systems

This paper deals with the input-to-state stability of time delay systems. It is not only for deterministic time delay systems, but also for stochastic time delay systems. It is drawn support from the stability of non-delay systems. Firstly, the definition of input-to-state stability of non-delay systems extended to input-to-state stability of time delay systems and stochastic input-to-state of non-delay systems extended to stochastic input-to-state stability of stochastic time delay systems. Secondly, by using lyapunov-krasovskii functional theory, the lyapunov theorems on ISS/SISS/P-SISS were given. Lastly, some examples will be introduced to illustrate the application of these theorems.