Variable Structure Control of Uncertain Dynamical Systems with Time-Varying Delay

Abstract

The problem of variable structure control of uncertain time-delay dynamical systems is discussed. Two types of sliding surfaces are considered, and a class of variable structure control strategies are proposed. It is shown that for the uncertainties satisfying the matching conditions, the resulting variable structure control systems are invariant, i.e. the systems are completely insensitive to such uncertainties. Some sufficient conditions are also derived such that the robust stability of the resulting variable structure control systems with unmatched uncertainties can be guaranteed. In addition, the time-varying delay is assumed only to be any bounded and continuous function, and all of the control laws, the sliding surfaces, and the sufficient conditions are independent of the delay. Therefore, the results obtained in the paper are also applicable to the systems with perturbed time-delay.