LMI stability conditions and stabilization of fractional-order systems with poly-topic and two-norm bounded uncertainties for fractional-order α: the 1 < α < 2 case

被引：9
|
作者：
Li, Sulan [1 ,2 ]
机构：
[1] Xidian Univ, Key Lab Elect Equipment Struct Design, Minist Educ, 2 Taibai Rd, Xian 710071, Shaanxi, Peoples R China
[2] Univ New South Wales, Sch Civil & Environm Engn, Sydney, NSW, Australia
来源：
COMPUTATIONAL & APPLIED MATHEMATICS | 2018年 / 37卷 / 04期
关键词：
LTI fractional-order system; Poly-topic uncertainty; Two-norm bounded uncertainty; Stability condition; Stabilization; ROBUST STABILITY; LINEAR-SYSTEMS; PERTURBATIONS; MODEL; CHAOS; MOTOR;
D O I：
10.1007/s40314-018-0610-x
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article addresses the problem of robust stability and stabilization for linear fractional-order system with poly-topic and two-norm bounded uncertainties, and focuses particularly on the case of a fractional order alpha such that 1 < alpha < 2. First, the robust asymptotical stable condition is presented. Second, the design method of the state feedback controller for asymptotically stabilizing such uncertain fractional order systems is derived. In the proposed approach, linear matrix inequalities formalism is used to check and design. Lastly, two simulation examples are given to validate the proposed theoretical results.
引用
收藏
页码：5000 / 5012
页数：13
相关论文
共 50 条
  • [21] H∞ control for singular fractional-order interval systems: The 0 &lt; α &lt; 1 case
    Zhang, Qing-Hao
    Lu, Jun-Guo
    ISA TRANSACTIONS, 2021, 110 : 105 - 116
  • [22] Positive real lemmas for singular fractional-order systems: the 0 &lt; α &lt; 1 case
    Zhang, Qing-Hao
    Lu, Jun-Guo
    IET CONTROL THEORY AND APPLICATIONS, 2020, 14 (18): : 2805 - 2813
  • [23] 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
  • [24] Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach
    Lu, Jun-Guo
    Chen, Guanrong
    IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (06) : 1294 - 1299
  • [25] Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α &lt; 2
    Lin, Ming-Shue
    Wu, Jenq-Lang
    Yung, Chee-Fai
    IEEE ACCESS, 2023, 11 : 122295 - 122301
  • [26] The adaptive synchronization of fractional-order chaotic system with fractional-order 1 &lt; q &lt; 2 via linear parameter update law
    Zhou, Ping
    Bai, Rongji
    NONLINEAR DYNAMICS, 2015, 80 (1-2) : 753 - 765
  • [27] Robust H∞ Control of Fractional-Order Switched Systems with Order 0 &lt; α &lt; 1 and Uncertainty
    Li, Bingxin
    Zhao, Xiangfei
    Liu, Yaowei
    Zhao, Xin
    FRACTAL AND FRACTIONAL, 2022, 6 (03)
  • [28] Robust stability and stabilization of fractional-order linear systems with polytopic uncertainties
    Chen, Liping
    Wu, Ranchao
    He, Yigang
    Yin, Lisheng
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 : 274 - 284
  • [29] Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties
    Lu, Jun-Guo
    Chen, YangQuan
    FRACTIONAL CALCULUS AND APPLIED ANALYSIS, 2013, 16 (01) : 142 - 157
  • [30] Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties
    Jun-Guo Lu
    YangQuan Chen
    Fractional Calculus and Applied Analysis, 2013, 16 : 142 - 157
12345