Robust Control and Stability Bound Analysis for a Class of LTI Fractional Order Uncertain Systems With 0 < α < 1

被引：1
作者：
Li, Sulan [1 ,2 ]
Zhu, Yunru [1 ,3 ]
Mi, Jianwei [1 ,2 ]
机构：
[1] Xidian Univ, Key Lab Elect Equipment Struct Design, Minist Educ, Xian 710071, Shaanxi, Peoples R China
[2] Xidian Univ, Shaanxi Key Lab Space Solar Power Stn Syst, Xian 710071, Shaanxi, Peoples R China
[3] Xidian Univ, Sch Mechanoelect Engn, Ctr Complex Syst, Xian 710071, Shaanxi, Peoples R China
来源：
IEEE ACCESS | 2019年 / 7卷
关键词：
Uncertainty; Stability analysis; Numerical stability; H infinity control; Robust stability; Symmetric matrices; Sufficient conditions; Fractional order system (FOS); < italic xmlns:ali="http; www; niso; org; schemas; ali; 1; 0; xmlns:mml="http; w3; 1998; Math; MathML" xmlns:xlink="http; 1999; xlink" xmlns:xsi="http; 2001; XMLSchema-instance"> H <; italic >-infinity bounded uncertainty; maximal bound; poly-topic uncertainty; stabilization; STABILIZATION; STABILIZABILITY;
D O I：
10.1109/ACCESS.2019.2943481
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This paper concentrates on the robust control and maximal bound analysis of uncertainty for the LTI fractional order system (FOS), which is subjected to poly-topic and H-infinity bounded uncertainties with 0 < alpha < 1. Firstly, two problems including robust stability analysis and stabilization are investigated. Subsequently, the method of how to determine the maximal uncertainty bound of such system is discussed, and the corresponding linear state feedback stabilizing controller is obtained together. The conditions in terms of linear matrix inequalities (LMI) for these problems mentioned above are concluded as four theorems. Finally, the advantage of the proposed methods is illustrated by two numerical examples.
引用
收藏
页码：140723 / 140733
页数：11
相关论文
共 36 条
  • [1] Adelipour S, 2014, T I MEAS CONTROL, V37, P1207
  • [2] On the concept of solution for fractional differential equations with uncertainty
    Agarwal, Ravi P.
    Lakshmikantham, V.
    Nieto, Juan J.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) : 2859 - 2862
  • [3] On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems
    Ahmed, E.
    El-Sayed, A. M. A.
    El-Saka, Hala A. A.
    [J]. PHYSICS LETTERS A, 2006, 358 (01) : 1 - 4
  • [4] Hurwitz stability analysis of fractional order LTI systems according to principal characteristic equations
    Alagoz, Buis Baykant
    [J]. ISA TRANSACTIONS, 2017, 70 : 7 - 15
  • [5] Brockett R.W., 2001, New issues in the mathematics of control, Mathematics unlimited-2001 and beyond, P189
  • [6] Stabilization of Uncertain Multi-Order Fractional Systems Based on the Extended State Observer
    Chen, Liping
    Chen, Gang
    Wu, Ranchao
    Tenreiro Machado, J. A.
    Lopes, Antonio M.
    Ge, Suoliang
    [J]. ASIAN JOURNAL OF CONTROL, 2018, 20 (03) : 1263 - 1273
  • [7] Convex Lyapunov functions for stability analysis of fractional order systems
    Chen, Weisheng
    Dai, Hao
    Song, Yanfei
    Zhang, Zhengqiang
    [J]. IET CONTROL THEORY AND APPLICATIONS, 2017, 11 (07) : 1070 - 1074
  • [8] Stability Analysis, Chaos Control of Fractional Order Vallis and El-Nino Systems and Their Synchronization
    Das, Subir
    Yadav, Vijay K.
    [J]. IEEE-CAA JOURNAL OF AUTOMATICA SINICA, 2017, 4 (01) : 114 - 124
  • [9] Robust static output feedback control synthesis for linear continuous systems with polytopic uncertainties
    Dong, Jiuxiang
    Yang, Guang-Hong
    [J]. AUTOMATICA, 2013, 49 (06) : 1821 - 1829
  • [10] Pseudo-state feedback stabilization of commensurate fractional order systems
    Farges, Christophe
    Moze, Mathieu
    Sabatier, Jocelyn
    [J]. AUTOMATICA, 2010, 46 (10) : 1730 - 1734
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