On Robust Dynamic State Feedback Stabilization of Variable Time-Delay Uncertain Systems

This note focuses on the robust asymptotic stabilization of linear uncertain dead-time systems with state-delay using the strategy of Dynamic Memoryless Controller. The delay is unknown and time-varying. The upper bound on the evolution rate of delay is arbitrary and not restricted to unity. The uncertainty taken into account is assumed to be of polytopic type. A less conservative delay-dependent condition in the form of Linear Matrix Inequalities (LMIs) is presented using Lyapunov-Krasovskii functional based approach. Auxiliary System based approach has been used and a sufficient condition for the robust stabilization is presented. Illustrative numerical examples and simulations are given to reflect the effectiveness of our results.