Mathematical control of complex systems

Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

Sliding mode adaptive state observation for time-delay uncertain nonlinear systems

In this paper a method to design robust adaptive sliding mode observers (ASMO) for a class of nonlinear time- delay systems with uncertainties, is proposed. The objective is to achieve insensitivity and robustness of the proposed sliding mode observer to matched disturbances. A novel systematic design method is synthesized to solve matching conditions and compute observer stabilizing gains. The Lyapunov-Krasovskii theorem is employed to prove the ultimate stability with arbitrary boundedness radius of the estimation error of the proposed filter. Finally, the ability of ASMO for fault reconstruction is studied

On designing observers for time-delay systems with nonlinear disturbances

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2002 Taylor & Francis LtdIn this paper, the observer design problem is studied for a class of time-delay nonlinear systems. The system under consideration is subject to delayed state and non-linear disturbances. The time-delay is allowed to be time-varying, and the non-linearities are assumed to satisfy global Lipschitz conditions. The problem addressed is the design of state observers such that, for the admissible time-delay as well as non-linear disturbances, the dynamics of the observation error is globally exponentially stable. An effective algebraic matrix inequality approach is developed to solve the non-linear observer design problem. Specifically, some conditions for the existence of the desired observers are derived, and an explicit expression of desired observers is given in terms of some free parameters. A simulation example is included to illustrate the practical applicability of the proposed theory.The work of Z. Wang was supported in part by the University of Kaiserslautern of Germany and the Alexander von Humboldt Foundation of Germany