Local <i>H</i>∞ Control for Continuous-Time T-S Fuzzy Systems via Generalized Non-Quadratic Lyapunov Functions

Abstract

This paper further develops a relaxed method to reduce conservatism in H∞ feedback control for continuous-time T-S fuzzy systems via a generalized non-quadratic Lyapunov function. Different from the results of some exisiting works, the generalized H∞ state feedback controller is designed. The relaxed stabilization conditions are obtained by applying Finsler’s lemma with the homogenous polynomial multipliers, and the H∞ performance is acquired by solving an optimization problem. In addition, the proposed method could be expanded to handle other control problems for fuzzy systems. Two examples are given to show the validity of the proposed results.

Keywords

• generalized non-quadratic Lyapunov function
• T-S fuzzy system
• feedback controller
• <i>H</i>∞ performance