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Mathematical Problems in Engineering
Volume 2015, Article ID 546835, 14 pages
Research Article

Delay-Dependent Finite-Time Controller Design for a Kind of Nonlinear Descriptor Systems via a T-S Fuzzy Model

1School of Science, Shenyang Jianzhu University, Shenyang 110168, China
2Trade Union Committee, Shenyang Jianzhu University, Shenyang 110168, China
3School of Science, University of Science and Technology Liaoning, Anshan 114051, China

Received 19 May 2015; Accepted 1 September 2015

Academic Editor: Xinggang Yan

Copyright © 2015 Baoyan Zhu 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.


Delay-dependent finite-time controller design problems are investigated for a kind of nonlinear descriptor system via a T-S fuzzy model in this paper. The solvable conditions of finite-time controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the performance to a prescribed disturbance attenuation level . The method given is the ability to eliminate the impulsive behavior caused by descriptor systems in a finite-time interval, which confirms the existence and uniqueness of solutions in the interval. By constructing a nonsingular matrix, we overcome the difficulty that results in an infeasible linear matrix inequality (LMI). Using the FEASP solver and GEVP solver of the LMI toolbox, we perform simulations to validate the proposed methods for a nonlinear descriptor system via the T-S fuzzy model, which shows the application of the T-S fuzzy method in studying the finite-time control problem of a nonlinear system. Meanwhile the method was also applied to the biological economy system to eliminate impulsive behavior at the bifurcation value, stabilize the loop-closed system in a finite-time interval, and achieve a performance level.