Output feedback control synthesis for non-linear time-delay systems using a sliding-mode observer

In this paper, a class of non-linear time-varying delay systems with non-linear uncertainties is considered, where the input is distributed to the system non-linearly. A sliding-mode observer is designed by constructively utilizing the structure of the uncertainties. The sliding motion associated with the error dynamics is uniformly asymptotically stable and insensitive to the uncertainties. Then, based on the observer, a non-linear discontinuous control scheme is synthesized to stabilize the system uniformly asymptotically. The Lyapunov–Razumikhin approach is used to deal with the time delay. Both the bound on the uncertainty and the known non-linear term are fully used in the observer and controller design to reduce conservatism. A numerical example is given to illustrate the proposed approach. Simulation results demonstrate the efficiency of the obtained results.