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H∞ Control of T-S Fuzzy Systems Using a Fuzzy Basis- Function-Dependent Lyapunov Function

퍼지 기저함수에 종속적인 Lyapunov 함수를 이용한 T-S 퍼지 시스템의 H∞ 제어

  • 최현철 (서울대학교 전기 컴퓨터공학부) ;
  • 좌동경 (아주대학교 전자공학부) ;
  • 홍석교 (아주대학교 전자공학부)
  • Published : 2008.07.01

Abstract

This paper proposes an $H_{\infty}$ controller design method for Takagi-Sugeno (T-S) fuzzy systems using a fuzzy basis-function-dependent Lyapunov function. Sufficient conditions for the guaranteed $H_{\infty}$ performance of the T-S fuzzy control system are given in terms of linear matrix inequalities (LMIs). These LMI conditions are further used for a convex optimization problem in which the $H_{\infty}-norm$ of the closed-loop system is to be minimized. To facilitate the basis-function-dependent Lyapunov function approach and thus improve the closed-loop system performance, additional decision variables are introduced in the optimization problem, which provide an additional degree-of-freedom and thus can enlarge the solution space of the problem. Numerical examples show the effectiveness of the proposed method.

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