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Abstract and Applied Analysis
Volume 2013, Article ID 141058, 16 pages
Research Article

Variable Structure Disturbance Rejection Control for Nonlinear Uncertain Systems with State and Control Delays via Optimal Sliding Mode Surface Approach

1School of Mathematics and Computer Science, Yunnan Nationalities University, Kunming 650500, China
2Key Laboratory in Software Engineering of Yunnan Province, Kunming 650091, China

Received 18 July 2013; Accepted 9 September 2013

Academic Editor: Valery Y. Glizer

Copyright © 2013 Jing Lei 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.


The paper considers the problem of variable structure control for nonlinear systems with uncertainty and time delays under persistent disturbance by using the optimal sliding mode surface approach. Through functional transformation, the original time-delay system is transformed into a delay-free one. The approximating sequence method is applied to solve the nonlinear optimal sliding mode surface problem which is reduced to a linear two-point boundary value problem of approximating sequences. The optimal sliding mode surface is obtained from the convergent solutions by solving a Riccati equation, a Sylvester equation, and the state and adjoint vector differential equations of approximating sequences. Then, the variable structure disturbance rejection control is presented by adopting an exponential trending law, where the state and control memory terms are designed to compensate the state and control delays, a feedforward control term is designed to reject the disturbance, and an adjoint compensator is designed to compensate the effects generated by the nonlinearity and the uncertainty. Furthermore, an observer is constructed to make the feedforward term physically realizable, and thus the dynamical observer-based dynamical variable structure disturbance rejection control law is produced. Finally, simulations are demonstrated to verify the effectiveness of the presented controller and the simplicity of the proposed approach.