Adaptive sliding mode control for uncertain time-delay systems

Based on the Lyapunov stability, an adaptive sliding mode controller for uncertain time-delay systems is presented Sliding mode motion of the closed-loop system from any initial states can asymptotically approach to zero in the finite time, which avoids need of the upper bound of perturbations. By applying free-weighting Matrices technique and delay transformation model, a delay-dependent sufficient condition is derived to guarantee the asymptotic stability of the closed-loop system. A numerical example is given to illustrate the feasibility of the proposed control methodology.