Robust sliding mode control of uncertain time delay systems

A robust sliding mode control design methodology is presented in this paper for a class of uncertain time delay systems. The systems are assumed to have structured, unmatched and time-varying parameter uncertainties as well as matched and bounded external disturbances. Delay-independent sufficient conditions for the design of a stable sliding manifold are given first in terms of an ARE and then via the Schur complement as linear matrix inequalities (LMIs). A controller guaranteeing convergence of the state trajectory to the sliding manifold is then developed and then generalized to account for uncertainties in the delay. A technique for the adaptation of controller gains is also presented. A Lyapunov method underlies both sliding manifold and controller design. A numerical example with simulation results illustrates the effectiveness of the methodology.