H∞ control design for uncertain linear systems with time-varying delays using LMI

A new delay-dependent approach for robust control of multiple time-varying delayed systems with uncertain parameters is proposed. The internal stability of the proposed controller is shown by proposing a new Lyapunov-Krasovskii functional. The upper bound of the delay and its time-derivative are explicitly used in designing the controller. No constraint is imposed on the time-delay functions. Hence, the closed-loop system performance is more robust and less conservative in terms of tolerating the effects of time-varying delays. Moreover, the proposed controller does not rely on restrictive assumptions on the rate of change of time-delay function, (i.e. tau < 1), which makes it applicable to fast time varying delayed systems. Finally, a robust state feedback controller is designed via Linear Matrix Inequality (LMI) technique. Unlike many previous methods, no parameter tuning is necessary to solve the resulting LMI conditions. Simulation results confirm that our proposed controller yields results that are more robust and less conservative as compared to existing methods in the literature.