Robust stability of fractional order system with polynomial uncertainties based on sum-of-squares approach

被引：3
|
作者：
Zheng, Shiqi [1 ,2 ]
Liang, Bingyun [1 ,2 ]
Liu, Feng [1 ,2 ]
Yang, Zichao [1 ,2 ]
Xie, Yuanlong [3 ]
机构：
[1] China Univ Geosci, Sch Automat, 388 Lumo Rd, Wuhan 430074, Peoples R China
[2] Hubei Key Lab Adv Control & Intelligent Automat C, Wuhan 430074, Peoples R China
[3] Huazhong Univ Sci & Technol, Wuhan, Peoples R China
来源：
JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2020年 / 357卷 / 12期
基金：
中国国家自然科学基金;
关键词：
INTERVAL SYSTEMS; CONTROLLERS; STABILIZATION;
D O I：
10.1016/j.jfranklin.2020.05.033
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 study of robust stability of fractional order system with polynomial uncertainties. Polynomial uncertainties means that the coefficients of the fractional system are polynomial functions of the parameters, and the uncertain parameters vary in semialgebraic set. The roots of the fractional order characteristic function are assigned in the shifted half plane. Therefore, the fractional system can maintain certain robustness and time domain performance. In order to check the robust stability of fractional order polynomial system, alternative methods are presented by using Sum of Squares (SOS) programs. Since SOS programs can be all written as Linear Matrix Inequalities (LMI) feasibility tests, our proposed method embraces the advantages of LMI techniques. Numerical examples are presented to illustrate the proposed results. (c) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
引用
收藏
页码：8035 / 8058
页数：24
相关论文
共 50 条
  • [41] Decomposition of a polynomial as a sum-of-squares of polynomials and the S-Procedure
    de Oliveira, Mauricio
    2005 44th IEEE Conference on Decision and Control & European Control Conference, Vols 1-8, 2005, : 1654 - 1659
  • [42] Applying Sum-of-Squares Decomposition Technique to Power System Robust Control Problem
    Chen, Mingyuan
    Li, Xiaocong
    Lagoa, Constantino M.
    Cong, Lanmei
    Xu, Junhua
    IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING, 2018, 13 (02) : 218 - 225
  • [43] Switching Control Strategy for DC-DC Converters Based on Polynomial Lyapunov Function and Sum-of-Squares Approach
    Ma, Wenjie
    Zhang, Bo
    Qiu, Dongyuan
    Sun, Huadong
    IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 2023, 70 (04) : 3663 - 3673
  • [44] A sum of squares approach to stability analysis of polynomial fuzzy systems
    Tanaka, Kazuo
    Yoshida, Hiroto
    Ohtake, Hiroshi
    Wang, Hua O.
    2007 AMERICAN CONTROL CONFERENCE, VOLS 1-13, 2007, : 2654 - +
  • [45] Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application
    Huang, D.
    Chernyshenko, S.
    Goulart, P.
    Lasagna, D.
    Tutty, O.
    Fuentes, F.
    PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2015, 471 (2183):
  • [46] Multidimensional stability test using sum-of-squares decomposition
    Dumitrescu, B
    2004 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL 3, PROCEEDINGS, 2004, : 545 - 548
  • [47] SUM-OF-SQUARES BASED OBSERVER DESIGN FOR POLYNOMIAL SYSTEMS WITH A KNOWN FIXED TIME DELAY
    Rehak, Branislav
    KYBERNETIKA, 2015, 51 (05) : 856 - 873
  • [48] A Novel Stabilization Condition for T-S Polynomial Fuzzy System with Time-delay: A Sum-of-Squares Approach
    Tsai, Shun-Hung
    Chen, Yu-An
    Chen, Yu-Wen
    Lo, Ji-Chang
    Lam, Hak-Keung
    2016 IEEE INTERNATIONAL CONFERENCE ON SYSTEMS, MAN, AND CYBERNETICS (SMC), 2016, : 1555 - 1560
  • [49] Design of State-Feedback Quadratic Regulator for Polynomial Systems Using Sum-of-Squares Approach
    Jennawasin, Tanagorn
    Banjerdpongchai, David
    2016 INTERNATIONAL AUTOMATIC CONTROL CONFERENCE (CACS), 2016, : 116 - 121
  • [50] Stability Analysis of Fluid Flows Using Sum-of-Squares
    Goulart, Paul J.
    Chernyshenko, Sergei I.
    2010 AMERICAN CONTROL CONFERENCE, 2010, : 2971 - 2976
12345