New sufficient conditions for stability analysis of time delay systems using dissipativity theory

Abstract

We extend the concepts of dissipativity and exponential dissipativity to provide new sufficient conditions for guaranteeing asymptotic stability of a time delay dynamical system. Specifically, representing a time delay dynamical system as a negative feedback interconnection of a finite-dimensional linear dynamical system and an infinite-dimensional time delay operator, we show that the time delay operator is dissipative. As a special case of this result we show that the storage functional of the dissipative delay operator involves an integral term identical to the integral term appearing in standard Lyapunov-Krasovskii functional. Finally, using stability of feedback interconnection results for dissipative systems, we develop new sufficient conditions for asymptotic stability of time delay dynamical systems. The overall approach provides an explicit framework for constructing Lyapunov-Krasovskii functionals as well as deriving new sufficient conditions for stability analysis of asymptotically stable time delay dynamical systems based on the dissipativity properties of the time delay operator.