Switched Systems Approach to State Bounding for Time Delay Systems

Abstract

This paper investigates the problems of reachable set estimation for dynamic systems with time-varying delay and random delay. Different from the traditional Lyapunov-Krasovskii functional method, a switched systems approach is adopted to study the reachable set estimation problem for time-varying delay systems. Through augmentation, time-varying delay systems can be transformed into switched delay-free systems. The reachable set of a time-varying delay system is estimated based on its corresponding augmented switched system. The number of decision variables in the obtained reachable set estimation condition is small compared with the Lyapunov-Krasovskii functional method. In addition, the problem of mean square estimation of the system state for random delay systems is also studied. The effectiveness of the theoretical findings is verified through several simulation examples.