Reducing the conservatism of LMI-based stabilisation conditions for TS fuzzy systems using fuzzy Lyapunov functions

被引：67

作者：

Faria, Flavio A. ^{[1
]}

Silva, Geraldo N. ^{[1
]}

Oliveira, Vilma A. ^{[2
]}

机构：

[1] UNESP Univ Estadual Paulista, Inst Biociencias Letras & Ciencias Exatas, BR-15054000 Sao Paulo, Brazil

[2] Univ Sao Paulo, Dept Engn Eletr, BR-13560970 Sao Paulo, Brazil

来源：

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE | 2013年 / 44卷 / 10期

基金：

巴西圣保罗研究基金会;

关键词：

TS fuzzy systems; fuzzy Lyapunov functions; stability analysis; PDC fuzzy controllers; linear matrix inequalities; H-INFINITY CONTROL; NONLINEAR-SYSTEMS; SUFFICIENT CONDITIONS; QUADRATIC STABILITY; IDENTIFICATION; DESIGN;

D O I：

10.1080/00207721.2012.670307

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented.

引用

页码：1956 / 1969

页数：14

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