Converse Lyapunov Theorem of Input-to-State Stability for Time-delay Systems

This paper is concerned with locally Lipschitz continuous converse Lyapunov theorem of input-to-state stability for time-delay systems. For time-delay systems with arbitrary measurable locally essentially bounded disturbances, it is shown that a locally Lipschitz continuous Lyapunov functional exists if these systems are robustly asymptotically stable. Under this result, the Lyapunov characterizations of input-to-state stability for time-delay systems are obtained.