A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi-Sugeno Fuzzy Systems

被引：94

作者：

Lee, Dong Hwan ^{[1
]}

Park, Jin Bae ^{[1
]}

Joo, Young Hoon ^{[2
]}

机构：

[1] Yonsei Univ, Dept Elect Engn, Seoul 120749, South Korea

[2] Kunsan Natl Univ, Dept Control & Robot Engn, Kunsan 573701, Chongbuk, South Korea

来源：

IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2011年 / 19卷 / 04期

关键词：

Continuous-time Takagi-Sugeno (T-S) fuzzy systems; fuzzy Lyapunov functions (FLFs); linear matrix inequality (LMI); nonlinear systems; stability; NONQUADRATIC STABILIZATION CONDITIONS; QUADRATIC STABILITY; NONLINEAR-SYSTEMS; MODELS; DESIGN; PERFORMANCE; FORM;

D O I：

10.1109/TFUZZ.2011.2142315

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

This paper presents a new fuzzy Lyapunov function (FLF) for the stability analysis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. Unlike conventional FLFs, the proposed one depends not only on the fuzzy weighting functions of the T-S fuzzy systems but on their first-order time derivatives as well. Based on the proposed FLF, a sufficient stability condition is derived in the form of linear matrix inequalities, depending on the upper bounds on the second-order time derivative of the fuzzy weighting functions, as well as the first-order ones. Finally, some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature.

引用

页码：785 / 791

页数：8

共 24 条

[1]

[Anonymous], 2002, NONLINEAR SYSTEMS

[2] Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form [J].

Ding, BC ;

Sun, HX ;

Yang, P .

AUTOMATICA, 2006, 42 (03) :503-508

[3] A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems [J].

Fang, Chun-Hsiung ;

Liu, Yung-Sheng ;

Kau, Shih-Wei ;

Hong, Lin ;

Lee, Ching-Hsiang .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2006, 14 (03) :386-397

[4] Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions [J].

Feng, G .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2003, 11 (05) :605-612

[5]

Gahinet P., 1995, LMI Control Toolbox

[6] Control Law Proposition for the Stabilization of Discrete Takagi-Sugeno Models [J].

Guerra, Thierry Marie ;

Kruszewski, Alexandre ;

Bernal, Miguel .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2009, 17 (03) :724-731

[7] LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form [J].

Guerra, TM ;

Vermeiren, L .

AUTOMATICA, 2004, 40 (05) :823-829

[8] Piecewise quadratic stability of fuzzy systems [J].

Johansson, M ;

Rantzer, A ;

Årzén, KE .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 1999, 7 (06) :713-722

[9] Effective digital implementation of fuzzy control systems based on approximate discrete-time models [J].

Kim, Do Wan ;

Park, Jin Bae ;

Joo, Young Hoon .

AUTOMATICA, 2007, 43 (10) :1671-1683

[10] New approaches to relaxed quadratic stability condition of fuzzy control systems [J].

Kim, E ;

Lee, H .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2000, 8 (05) :523-534

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