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Mathematical Problems in Engineering
Volume 2015, Article ID 926762, 7 pages
Research Article

Integral Sliding Mode Control of Lur’e Singularly Perturbed Systems

1School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China
2Center for Applied and Interdisciplinary Mathematics, Department of Mathematics, East China Normal University, Shanghai 200241, China

Received 1 April 2015; Revised 23 August 2015; Accepted 24 August 2015

Academic Editor: Antonios Tsourdos

Copyright © 2015 Yanyan Wang and Wei Liu. 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.


This paper investigates the integral sliding mode control problem for Lur’e singularly perturbed systems with sector-constrained nonlinearities. First, we design a proper sliding manifold such that the motion of closed-loop systems with a state feedback controller along the manifold is absolutely stable. To achieve this, we give a matrix inequality-based absolute stability criterion; thus the above problem can be converted into a matrix inequality feasibility problem. In addition, the gain matrix can also be derived by solving the matrix inequality. Then, a discontinuous control law is synthesized to force the system state to reach the sliding manifold and stay there for all subsequent time. Finally, some numerical examples are given to illustrate the effectiveness of the proposed results.