LMI stability conditions for fractional order systems

被引：355
|
作者：
Sabatier, Jocelyn [1 ]
Moze, Mathieu [1 ]
Farges, Christophe [1 ]
机构：
[1] Univ Bordeaux 1, CNRS, IMS Lab, LAPS CRONE Grp,UMR 5218, F-33405 Talence, France
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2010年 / 59卷 / 05期
关键词：
Fractional systems; Stability; Linear Matrix Inequalities; ROBUST STABILITY; DELAY SYSTEMS;
D O I：
10.1016/j.camwa.2009.08.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
After an overview of the results dedicated to stability analysis of systems described by differential equations involving fractional derivatives, also denoted fractional order systems, this paper deals with Linear Matrix Inequality (LMI) stability conditions for fractional order systems. Under commensurate order hypothesis, it is shown that a direct extension of the second Lyapunov's method is a tedious task. If the fractional order v is such that 0 nu < 1, the stability domain is not a convex region of the complex plane. However, through a direct stability domain characterization, three LMI stability analysis conditions are proposed. The first one is based on the stability domain deformation and the second one on a characterization of the instability domain (which is convex). The third one is based on generalized LMI framework. These conditions are applied to the gain margin computation of a CRONE suspension. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1594 / 1609
页数：16
相关论文
共 50 条
  • [21] LMI-based sufficient conditions for robust stability and stabilization of LTI-fractional-order systems subjected to interval and polytopic uncertainties
    Adelipour, S.
    Abooee, A.
    Haeri, M.
    TRANSACTIONS OF THE INSTITUTE OF MEASUREMENT AND CONTROL, 2015, 37 (10) : 1207 - 1216
  • [22] Fractional Order Stability of Systems
    Senol, Bilal
    Matusu, Radek
    Gul, Emine
    2017 INTERNATIONAL ARTIFICIAL INTELLIGENCE AND DATA PROCESSING SYMPOSIUM (IDAP), 2017,
  • [23] Stability of Fractional Order Systems
    Rivero, Margarita
    Rogosin, Sergei V.
    Tenreiro Machado, Jose A.
    Trujillo, Juan J.
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
  • [24] Order-dependent LMI-based stability and stabilization conditions for fractional-order time-delay systems using small gain theorem
    Jin, Xiao-Chuang
    Lu, Jun-Guo
    INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, 2022, 32 (11) : 6484 - 6506
  • [25] Stabilization of Singular Fractional-Order Systems : An LMI Approach
    N'Doye, Ibrahima
    Zasadzinski, Michel
    Darouach, Mohamed
    Radhy, Nour-Eddine
    18TH MEDITERRANEAN CONFERENCE ON CONTROL AND AUTOMATION, 2010, : 209 - 213
  • [26] Alternative LMI Characterizations for Fractional-order Linear Systems
    Ding Dongsheng
    Qi Donglian
    Wang Qiao
    2014 33RD CHINESE CONTROL CONFERENCE (CCC), 2014, : 4246 - 4251
  • [27] Robust stability and stabilization of fractional-order linear systems with nonlinear uncertain parameters: An LMI approach
    Xing, Sheng Yan
    Lu, Jun Guo
    CHAOS SOLITONS & FRACTALS, 2009, 42 (02) : 1163 - 1169
  • [28] Stability analysis of fractional-order neural networks: An LMI approach
    Yang, Ying
    He, Yong
    Wang, Yong
    Wu, Min
    NEUROCOMPUTING, 2018, 285 : 82 - 93
  • [29] Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems
    Lenka, Bichitra Kumar
    Banerjee, Soumitro
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2018, 56 : 365 - 379
  • [30] LMI stability conditions and stabilization of fractional-order systems with poly-topic and two-norm bounded uncertainties for fractional-order α: the 1 &lt; α &lt; 2 case
    Li, Sulan
    COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04): : 5000 - 5012
12345