Robust stability analysis and synthesis of linear time-delay systems via LMIs

In this paper, the problem of robust stability analysis and synthesis of time-delay systems is investigated. Delay is assumed to be time varying and the system is supposed to be linear with polytopic uncertainties. A new type of Lyapunov-Krasovskii functional is proposed. The resulting delay-dependent stability conditions in from of LMIs turn to be less conservative than the existing conditions. The proposed stability criteria is then employed to design a state-feedback controller for the delayed systems such that stability of the closed-loop system for the maximum amount of delay is guaranteed. The resulting LMI conditions are expressed in terms of a known upper bound for delay. The performance and reduced conservatism of the proposed LMI conditions are illustrated via two numerical examples.