Sliding mode observer based control for a class of nonlinear time delay systems with delayed uncertainties

In this paper, a class of nonlinear time varying delay systems is considered. A sliding mode observer is proposed by employing the structure of the uncertainty such that the sliding motion associated with the error dynamics is uniformly asymptotically stable. Then, based on the observer, a nonlinear discontinuous control scheme is presented to stabilise the system uniformly asymptotically. The Razuminkin Lyapunov approach is used to deal with the time delay. The accessible part of both the bounds and the nonlinear terms is separated and used in the control design to reduce conservatism. A numerical example is given to illustrate the proposed approach.