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
收藏
页码：707 / 714
页数：8
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