LMI-Based Stability Analysis for Piecewise Multi-affine Systems

被引：13

作者：

Nguyen, Anh-Tu ^{[1
]}

Sugeno, Michio ^{[2
]}

Campos, Victor ^{[3
]}

Dambrine, Michel ^{[4
]}

机构：

[1] Inst Rech Commun & Cybernet Nantes IRCCyN, CNRS, UMR 6597, Nantes, France

[2] Tokyo Inst Technol, Tokyo 1528550, Japan

[3] Univ Fed Ouro Preto, Dept Elect Engn, BR-35400000 Joao Monlevade, Brazil

[4] CNRS, UMR 8201, Lab Ind & Human Automat Control Mech Engn & Comp, Valenciennes, France

来源：

IEEE TRANSACTIONS ON FUZZY SYSTEMS | 2017年 / 25卷 / 03期

关键词：

Fuzzy systems; linear matrix inequalities (LMIs); piecewise Lyapunov functions; piecewise multi-affine (PMA) systems; singleton consequents; stability analysis; FUZZY LOGIC-CONTROLLER; DESIGN;

D O I：

10.1109/TFUZZ.2016.2566798

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 provides a computational method to study the asymptotic stability of piecewise multi-affine (PMA) systems. Such systems stem from a class of fuzzy systems with singleton consequents and can be used to approximate any smooth nonlinear system with arbitrary accuracy. Based on the choice of piecewise Lyapunov functions, stability conditions are expressed as a feasibility test of a convex optimization with linear matrix inequality constraints. The basic idea behind these conditions is to exploit the parametric expressions of PMA systems by means of Finsler's lemma. Numerical examples are given to point out the effectiveness of the proposed method.

引用

页码：707 / 714

页数：8

共 50 条

[41] Robust Finite-Time H∞ Control of a Class of Disturbed Systems using Lmi-Based Approach [J].

Zhang, Xiaoyu ;

Zhong, Jihong ;

Zhang, Quan ;

Ma, Kemao .

ASIAN JOURNAL OF CONTROL, 2017, 19 (02) :575-586

[42] LMI-Based Adaptive Tracking Control for Parametric Strict-Feedback Systems [J].

Lian, Kuang-Yow ;

Tu, Hui-Wen .

IEEE TRANSACTIONS ON FUZZY SYSTEMS, 2008, 16 (05) :1245-1258

[43] On LMI-based sliding mode control for uncertain discrete-time systems [J].

Argha, Ahmadreza ;

Li, Li ;

Su, Steven W. ;

Hung Nguyen .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2016, 353 (15) :3857-3875

[44] LMI-based H∞ control for linear singular discrete systems: a novel method [J].

Dong, Xin-Zhuang .

IET CONTROL THEORY AND APPLICATIONS, 2013, 7 (16) :2028-2036

[45] Non-synchronized H∞ Estimation of Discrete-Time Piecewise Affine Systems: An LMI Approach [J].

Liu, Zhiyuan ;

Gao, Yahui ;

Chen, Hong .

ICIA: 2009 INTERNATIONAL CONFERENCE ON INFORMATION AND AUTOMATION, VOLS 1-3, 2009, :585-+

[46] Asymptotic Stability of Piecewise Affine Systems With Filippov Solutions via Discontinuous Piecewise Lyapunov Functions [J].

Iervolino, Raffaele ;

Trenn, Stephan ;

Vasca, Francesco .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2021, 66 (04) :1513-1528

[47] LMI-based stability and performance conditions for continuous-time nonlinear systems in Takagi-Sugeno's form [J].

Lam, H. K. ;

Leung, Frank H. E. .

IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS, 2007, 37 (05) :1396-1406

[48] LMI-Based Tracking Control of the Fuzzy Systems: Smooth Compositions Work Better [J].

Sadjadi, Ebrahim Navid .

INTERNATIONAL JOURNAL OF FUZZY SYSTEMS, 2024, 26 (02) :449-462

[49] No Excuses to Avoid Observing Unstable Nonlinear Systems: An LMI-Based Discontinuous Solution [J].

Quintana, Daniel ;

Estrada-Manzo, Victor ;

Bernal, Miguel .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2024, 69 (10) :7136-7143

[50] On LMI-based algorithm for strictly positive real systems with static output feedback [J].

Teixeira, Marcelo C. M. ;

Covacic, Marcio R. ;

Gaino, Ruberlei ;

Assuncao, Edvaldo ;

Cardim, Rodrigo ;

Lazarini, Adalberto Z. N. .

2022 16TH INTERNATIONAL WORKSHOP ON VARIABLE STRUCTURE SYSTEMS (VSS), 2022, :15-21

← 1 2 3 4 5 →