Robust delay-dependent stabilization of uncertain time-delay systems by variable structure control

In this paper, the problem of robust sliding mode controller design for uncertain multivariable systems with several fixed state delays is addressed. A new combined sliding mode controller is considered and designed for the delay-dependent stabilization of perturbed sliding time-delay systems with matched parameter uncertainties and external disturbances. Delay-dependent stability and sliding mode existence conditions are derived by using modified Lyapunov-Krasovskii functional and formulated in terms of LMI. The allowable upper bounds on the time-delay are determined from the LMI stability conditions. A numerical example is given to illustrate the usefulness of the proposed design method.