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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 896515, 13 pages
Research Article

Fuzzy Control for Nonlinear Singular Markovian Jump Systems with Time Delay

1College of Mathematics and Physics, Bohai University, Jinzhou, Liaoning 121013, China
2Institute of Systems Science, Northeastern University, Shenyang, Liaoning 110819, China
3School of Science, Shenyang University of Technology, Shenyang, Liaoning 110870, China
4College of Science, Shenyang Jianzhu University, Shenyang, Liaoning 110168, China

Received 7 January 2015; Accepted 20 April 2015

Academic Editor: P. Balasubramaniam

Copyright © 2015 Li Li 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.


This paper investigates the problem of fuzzy control for a class of nonlinear singular Markovian jump systems with time delay. This class of systems under consideration is described by Takagi-Sugeno (T-S) fuzzy models. Firstly, sufficient condition of the stochastic stabilization by the method of the augmented matrix is obtained by the state feedback. And a designed algorithm for the state feedback controller is provided to guarantee that the closed-loop system not only is regular, impulse-free, and stochastically stable but also satisfies a prescribed performance for all delays not larger than a given upper bound in terms of linear matrix inequalities. Then fuzzy control for this kind of systems is also discussed by the static output feedback. Finally, numerical examples are given to illustrate the validity of the developed methodology.