Robust H∞ control for fuzzy systems with Frobenius norm-bounded uncertainties

被引：30
作者：
Lo, JC [1 ]
Lin, ML
机构：
[1] Natl Cent Univ, Fac Mech Engn, Chungli 320, Taiwan
[2] LITE ON IT Corp, Prod Design Div 1, Elect Engn Dept 1, Taipei 114, Taiwan
来源：
IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2006年 / 14卷 / 01期
关键词：
bounded real lemma; Frobenius norm; H-infinity control; linear matrix inequality (LMI); Takagi-Sugeno (T-S) fuzzy model;
D O I：
10.1109/TFUZZ.2005.861602
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this paper, we investigate the problem of robust H-infinity performance and stabilization for a class of uncertain fuzzy systems with Frobenius norm-bounded parameter uncertainties in all system matrices. Both continuous- and discrete-time uncertain fuzzy systems are considered under a unified treatment called bounded real lemma for fuzzy systems. Unlike the bounded real lemma in the linear theory of robust H-infinity control where necessary and sufficient conditions were obtained, only sufficient condition based on Lyapunov method is shown. Furthermore, connection between robust H-infinity problems involving uncertainty and standard uncertainly-free H-infinity problems is established via matrix algebra. As for controller synthesis, a state feedback fuzzy control law is designed via relaxed linear matrix inequality (LMI) formulations.
引用
收藏
页码：1 / 15
页数：15
相关论文
共 36 条
[1]  
Boy S., 1994, Linear MatrixInequalities in System and Control Theory
[2]   Robust H∞ disturbance attenuation for a class of uncertain discrete-time fuzzy systems [J].
Cao, YY ;
Frank, PM .
IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2000, 8 (04) :406-415
[3]  
Chen BS, 2000, IEEE T FUZZY SYST, V8, P249, DOI 10.1109/91.855915
[4]   ON THE DISCRETE-TIME BOUNDED REAL LEMMA WITH APPLICATION IN THE CHARACTERIZATION OF STATIC STATE FEEDBACK H-INFINITY CONTROLLERS [J].
DESOUZA, CE ;
XIE, LH .
SYSTEMS & CONTROL LETTERS, 1992, 18 (01) :61-71
[5]   MIXED-NORM H2/H-INFINITY REGULATION AND ESTIMATION - THE DISCRETE-TIME CASE [J].
HADDAD, WM ;
BERNSTEIN, DS ;
MUSTAFA, D .
SYSTEMS & CONTROL LETTERS, 1991, 16 (04) :235-247
[6]   GENERALIZED RICCATI-EQUATIONS FOR THE FULL-ORDER AND REDUCED-ORDER MIXED-NORM H2/H-INFINITY [J].
HADDAD, WM ;
BERNSTEIN, DS .
SYSTEMS & CONTROL LETTERS, 1990, 14 (03) :185-197
[7]   Computation of piecewise quadratic Lyapunov functions for hybrid systems [J].
Johansson, M ;
Rantzer, A .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1998, 43 (04) :555-559
[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]   ROBUST STABILIZATION OF UNCERTAIN LINEAR-SYSTEMS - QUADRATIC STABILIZABILITY AND H INFINITY-CONTROL THEORY [J].
KHARGONEKAR, PP ;
PETERSEN, IR ;
ZHOU, KM .
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1990, 35 (03) :356-361
[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
1234