Sliding mode observer based-controller design for nonlinear systems with time varying delay

Abstract

A class of nonlinear time varying delay systems in the presence of time delay uncertainties is considered in this chapter. The entries of the system input distribution matrix may be nonlinear functions of the outputs and time. Under mild limitations on the uncertainty, an observer is synthesised using sliding mode techniques such that the error dynamics are ultimately uniformly bounded in the presence of uncertainties and time delay. Then, a nonlinear control scheme is developed based on the estimated states, and a set of sufficient conditions is presented such that the corresponding closed-loop systems are uniformly ultimately bounded, using the wellknown Lyapunov-Razumikhin approach. It is not required that the structure of the uncertainty be known. Finally, a numerical example is presented to demonstrate the approach and simulation results show the effectiveness of the developed paradigm.