Design of a Robust Dynamic State Feedback Controller for Systems with Time-Varying State Delays

This note highlights the asymptotic stability of linear dead-time systems with state-delay. The delay is time-varying, unknown and bounded. A less conservative delay-dependent linear matrix inequality (LMI) method is presented based on using a new Lyapunov-Krasovskii functional. Auxiliary system based approach has been used and a sufficient condition for the asymptotic stability is presented. The result obtained includes information on the size of the delay, and is therefore a delay-dependent stability condition. Also a state feedback dynamic controller is designed for the stabilization of the system. Illustrative numerical examples are given to reflect the effectiveness of our results.