On improved robust stabilization of uncertain systems with unknown input delay

This paper investigates the robust stabilization problem for uncertain systems with unknown input delay based on the reduction method. Two types of the unknown input delay are considered: one is constant; the other is continuous and may vary fast. Sufficient matrix inequalities conditions for stabilizability of such systems are derived via Lyapunov functionals and the descriptor system approach to time-delay systems. An algorithm involving convex optimization is proposed to design a delayed state feedback controller such that the system can be stabilized for all admissible uncertainties. Two illustrative examples are presented to show the effectiveness of the proposed algorithm.