An LMI approach to adaptive robust tracker design for uncertain nonlinear systems with time-delays and input nonlinearities

In this paper, the adaptive robust tracking and model following controller is designed for the uncertain nonlinear systems with disturbances, time-delays and input nonlinearities. A novel control law based on the linear matrix inequalities is proposed for the tracking control of the nonlinear systems with Lipschitz nonlinearities. The selection procedure of the nonlinear integral sliding surface and the existence of the proposed sliding mode are two significant subjects, which have been addressed. This controller guarantees that the tracking error decreases asymptotically to the origin in the presence of time-varying perturbations. By elimination of the reaching mode of the sliding surface, the robustness performance against perturbations is guaranteed right from the initial instant. Furthermore, the knowledge of the upper bounds of the uncertainties, disturbances and time-delays is not required to be determined. Simulation results are provided to illustrate the efficiency of the presented technique compared to the previous methods.