Delay-independent sliding mode control of nonlinear time-delay systems

In this paper, adaptive sliding mode control is presented for a class of parametric-strict-feed back nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties from unknown time delays are compensated for so that the proposed control scheme is delay-independent. Controller singularity problems are solved by employing practical control and regrouping unknown parameters. By using novel differentiable approximation, sliding mode control and practical control can be carried out in the backstepping design. It is proved that the proposed systematic backstepping design method is able to guarantee global uniformly ultimately boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.