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

• Main Authors: Baoyan Zhu, Jingjun Zhang, Daqing Zhang, Aibin Liu
• Format: Article
• Language: English
• Published: Hindawi Limited 2015-01-01
• Series: Mathematical Problems in Engineering
• Online Access: http://dx.doi.org/10.1155/2015/546835

Delay-dependent finite-time H∞ 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 H∞ controller are given to guarantee that the loop-closed system is impulse-free and finite-time bounded and holds the H∞ performance to a prescribed disturbance attenuation level γ. 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 H∞ performance level.