Robust variable structure control for uncertain systems with multiple time delays

In this paper, a robust variable structure control (VSC) strategy is presented for stabilizing the uncertain systems with multiple time delays where the uncertainty in the state model does not satisfy the matching condition. Based on the Bellman-Gronwall theorem, we provide a sufficient condition for the existence of switching hyperplane and we give an explicit formula of switching hyperplant guaranteeing the asymptotic stability of the reduced-order equivalent system dynamics restricted to the switching hyperplane. Furthermore, by means of the Lyapunov stability theory and norm technique, we derive an approximating continuous VSC law for uncertain systems with multiple time delays and mismatched uncertainties which are difficult to deal with by using conventional design approaches. Finally, an example is given to illustrate the design procedure and results of proposed approach.