High-gain sliding mode observers for a class of nonlinear uncertain delay systems

Abstract

This paper proposes an observer for the class of triangular nonlinear systems including the model uncertainty, with constant delays in the state and input equations. It is assumed that the nonlinear perturbations satisfy the Lipschitz condition and the uncertain part is bounded. The main idea is based on the designing a high-gain observer in combination with the sliding mode observer which leads to a robust high-gain observer that has not been sufficiently studied previously. A compensation term is included in the observer dynamics that is designed based on the solution of a Lyapunov inequality. For stability analysis, if the matching condition is satisfied, by using a suitable Lyapunov-Krasovski functional, simple sufficient conditions are provided that guarantees the observation error converges to the origin asymptotically. The simulation results for a nonlinear system in triangular form illustrate the effectiveness of the proposed approach.