Robust Sliding Mode Control of Multivariable Time-Delay Systems

In this paper, the problem of sliding mode controller design for uncertain multi-input systems with several fixed state delays is addressed. A combined sliding mode controller is considered and it is designed for the stabilization of perturbed multi-input time-delay systems with matched parameter uncertainties and external disturbances. Delay-independent stability conditions are derived by using Lyapunov-Krasovskii functional method and formulated in terms of LMI. The sliding mode existence conditions are also Studied by choosing a suitable Lyapunov function. The stability and sliding conditions arc consistent. Three numerical examples with simulation results are given to illustrate the usefulness of the proposed design method.