LMI-Based Stability Analysis of Fuzzy-Model-Based Control Systems Using Approximated Polynomial Membership Functions

被引：51

作者：

Narimani, Mohammand ^{[1
]}

Lam, H. K. ^{[1
]}

Dilmaghani, R. ^{[1
]}

Wolfe, Charles ^{[2
]}

机构：

[1] Kings Coll London, Div Engn, London WC2R 2LS, England

[2] Guys & St Thomas Natl Hlth Serv Fdn Trust, R&D, London SE1 7EH, England

来源：

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS | 2011年 / 41卷 / 03期

基金：

英国工程与自然科学研究理事会;

关键词：

Fuzzy control; linear matrix inequality (LMI); membership-function-shape-dependent stability conditions; Takagi-Sugeno (T-S) fuzzy model; NONLINEAR-SYSTEMS; RELAXED STABILITY; UNCERTAIN GRADES; DESIGN; PERFORMANCE; STABILIZATION; IDENTIFICATION; OBSERVERS; SUBJECT;

D O I：

10.1109/TSMCB.2010.2086443

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Relaxed linear-matrix-inequality-based stability conditions for fuzzy-model-based control systems with imperfect premise matching are proposed. First, the derivative of the Lyapunov function, containing the product terms of the fuzzy model and fuzzy controller membership functions, is derived. Then, in the partitioned operating domain of the membership functions, the relations between the state variables and the mentioned product terms are represented by approximated polynomials in each subregion. Next, the stability conditions containing the information of all subsystems and the approximated polynomials are derived. In addition, the concept of the S-procedure is utilized to release the conservativeness caused by considering the whole operating region for approximated polynomials. It is shown that the well-known stability conditions can be special cases of the proposed stability conditions. Simulation examples are given to illustrate the validity of the proposed approach.

引用

页码：713 / 724

页数：12

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