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
相关论文
共 50 条
  • [31] Controller Synthesis for Piecewise-Affine Time-Delay Slab Systems Based on Invariant Sets: An LMI Approach
    Kaynama, Sina
    Moarref, Miad
    Rodrigues, Luis
    [J]. 2013 AMERICAN CONTROL CONFERENCE (ACC), 2013, : 37 - 42
  • [32] Exponential Stability of Continuous-Time Piecewise Affine Systems
    Cabral, L.
    Valmorbida, G.
    da Silva Jr, J. M. Gomes
    [J]. IEEE CONTROL SYSTEMS LETTERS, 2024, 8 : 1649 - 1654
  • [33] An LMI Approach to Stability Analysis of Coupled Parabolic Systems
    Wakaiki, Masashi
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2020, 65 (01) : 404 - 411
  • [34] An LMI-based controller synthesis for periodic trajectories in a class of nonlinear systems
    Basso, M
    Genesio, R
    Tesi, A
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2002, 47 (10) : 1740 - 1744
  • [35] Antiwindup for stable linear systems with input saturation: An LMI-based synthesis
    Grimm, G
    Hatfield, J
    Postlethwaite, I
    Teel, AR
    Turner, MC
    Zaccarian, L
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (09) : 1509 - 1525
  • [36] LMI-based Control Synthesis for Continuous-time T-S Fuzzy Systems
    Wang, Dong
    Chang, Xiao-Heng
    [J]. PROCEEDINGS OF THE 2012 24TH CHINESE CONTROL AND DECISION CONFERENCE (CCDC), 2012, : 2707 - 2711
  • [37] LMI-based robust admissible control for uncertain singular delta operator systems
    Dong, Xin-Zhuang
    [J]. INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2015, 46 (12) : 2101 - 2110
  • [38] LMI-Based Exponential Estimates for Time-Delay Nonlinear Descriptor Systems
    Arceo, Juan Carlos
    Villafuerte, Raul
    Estrada-Manzo, Victor
    Bernal, Miguel
    [J]. IFAC PAPERSONLINE, 2018, 51 (10): : 139 - 144
  • [39] LMI-BASED ROBUST CONTROL OF UNCERTAIN NONLINEAR SYSTEMS VIA POLYTOPES OF POLYNOMIALS
    Sanchez, Marcelino
    Bernal, Miguel
    [J]. INTERNATIONAL JOURNAL OF APPLIED MATHEMATICS AND COMPUTER SCIENCE, 2019, 29 (02) : 275 - 283
  • [40] LMI-based H? boundary practical consensus control for nonlinear multi-agent systems with actuator saturation
    Zhong, Jiaqi
    Feng, Yan
    Zeng, Cheng
    [J]. ISA TRANSACTIONS, 2023, 135 : 261 - 271
12345