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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 614878, 9 pages
http://dx.doi.org/10.1155/2013/614878
Research Article

Sliding Mode Control Based on Observer for a Class of State-Delayed Switched Systems with Uncertain Perturbation

School of Automation, Harbin University of Science and Technology, Harbin, Heilongjiang 150080, China

Received 10 December 2012; Revised 24 February 2013; Accepted 24 February 2013

Academic Editor: Ligang Wu

Copyright © 2013 Zhaolan He 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.

Abstract

This paper is concerned with a state observer-based sliding mode control design methodology for a class of continuous-time state-delayed switched systems with unmeasurable states and nonlinear uncertainties. The advantages of the proposed scheme mainly lie in which it eliminates the need for state variables to be full accessible and parameter uncertainties to be satisfied with the matching condition. Firstly, a state observer is constructed, and a sliding surface is designed. By matrix transformation techniques, combined with Lyapunov function and sliding surface function, a sufficient condition is given to ensure asymptotic stability of the overall closed-loop systems composed of the observer dynamics and the estimation error dynamics. Then, reachability of sliding surface is investigated. At last, an illustrative numerical example is presented to prove feasibility of the proposed approaches.