Robust control of delay systems: a sliding mode control design via LMI

This paper considers the sliding mode control of uncertain systems with single or multiple, constant or time-varying state-delays, submitted to additive perturbations. The sliding surface is designed so to maximize the calculable set of admissible delays. The conditions for the existence of the sliding regime are studied by using Lyapunov–Krasovskii functionals and Lyapunov-Razumikhin functions. LMIs are used for the optimization procedure. Two examples illustrate the proposed method.