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

页码：1594 / 1609

页数：16

共 50 条

[41] Stability of fractional order switching systems
Hassan HosseinNia, S.
Tejado, Ines
Vinagre, Bias M.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 66 (05) : 585 - 596
[42] Fractional Order Hybrid Systems and Their Stability
HosseinNia, S. Hassan
Tejado, Ines
Vinagre, Blas M.
PROCEEDINGS OF THE 2013 14TH INTERNATIONAL CARPATHIAN CONTROL CONFERENCE (ICCC), 2013, : 128 - 133
[43] Robust stability conditions of fractional order discrete-time linear systems
Ruszewski, Andrzej
2017 22ND INTERNATIONAL CONFERENCE ON METHODS AND MODELS IN AUTOMATION AND ROBOTICS (MMAR), 2017, : 543 - 547
[44] Novel Stability and Stabilization Conditions for Fractional-Order Systems With Mixed Delays
Chen, Yi-Nan
Lu, Jun-Guo
Zhang, Qing-Hao
Zhu, Zhen
MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2025, 48 (06) : 6253 - 6262
[45] LMI conditions for global asymptotic stability of a second order hopfieldneural networks
Chang, Ru
Xia, Maohui
Chang, Tingting
Ji, Wei
ICIC Express Letters, 2010, 4 (02): : 533 - 537
[46] Stability and Stabilization of Singular Systems: Strict LMI Sufficient Conditions
Ziiang Xuefeng
PROCEEDINGS OF THE 10TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA 2012), 2012, : 1052 - 1055
[47] Robust stability and stabilization of hybrid fractional-order multi-dimensional systems with interval uncertainties: An LMI approach
Zhu, Zhen
Lu, Jun-Guo
APPLIED MATHEMATICS AND COMPUTATION, 2021, 401
[48] LMI-Based Robust Stability Analysis of Discrete-Time Fractional-Order Systems With Interval Uncertainties
Zhu, Zhen
Lu, Jun-Guo
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2021, 68 (04) : 1671 - 1680
[49] LMI synchronization conditions for variable fractional-order one-sided Lipschitz chaotic systems with gain fluctuations
Chen, Liping
Liu, Chuang
Lopes, Antonio M.
Lin, Yong
Liu, Yingxiao
Chen, YangQuan
CHAOS SOLITONS & FRACTALS, 2024, 189
[50] Consensus of fractional-order multi -agent systems via LMI approach
Ji, Yude
Liu, Yuejuan
Guo, Yanping
PROCEEDINGS OF THE 30TH CHINESE CONTROL AND DECISION CONFERENCE (2018 CCDC), 2018, : 907 - 912

← 1 2 3 4 5 →