An improved result on reachable set estimation and synthesis of time-delay systems

In this paper, the problems of reachable set estimation and synthesis of time-delay systems are investigated. By introducing the non-uniform delay-partitioning method and the triple integral technique, an improved reachable set estimation condition is proposed in terms of linear matrix inequality. Based on the criterion, a sufficient condition for the existence of a state-feedback controller is established to render the reachable set of the closed-loop system be bounded by a given ellipsoid. Two numerical examples are given to demonstrate the effectiveness of the obtained results.