Robust Stabilization of Input-Delayed Systems Subject to Parametric Uncertainties

The robust stabilization problem for uncertain systems with unknown input delay based on the reduction method is studied in this paper. Two types of the unknown input delay are considered: one is constant; the other one is continuous and may vary fast. Sufficient matrix inequalities conditions for the stabilizability of such systems are derived via Lyapunov functionals and descriptor 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. The usefulness of the proposed algorithm is demonstrated by a numerical example.