A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 3 Issue 4
Oct.  2016

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 6.171, Top 11% (SCI Q1)
    CiteScore: 11.2, Top 5% (Q1)
    Google Scholar h5-index: 51, TOP 8
Turn off MathJax
Article Contents
Baris Baykant Alagoz, "A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 411-421, Oct. 2016.
Citation: Baris Baykant Alagoz, "A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials," IEEE/CAA J. Autom. Sinica, vol. 3, no. 4, pp. 411-421, Oct. 2016.

A Note on Robust Stability Analysis of Fractional Order Interval Systems by Minimum Argument Vertex and Edge Polynomials

More Information
  • By using power mapping (s=vm), stability analysis of fractional order polynomials was simplified to the stability analysis of expanded degree integer order polynomials in the first Riemann sheet. However, more investigation is needed for revealing properties of power mapping and demonstration of conformity of Hurwitz stability under power mapping of fractional order characteristic polynomials. Contributions of this study have two folds:Firstly, this paper demonstrates conservation of root argument and magnitude relations under power mapping of characteristic polynomials and thus substantiates validity of Hurwitz stability under power mapping of fractional order characteristic polynomials. This also ensures implications of edge theorem for fractional order interval systems. Secondly, in control engineering point of view, numerical robust stability analysis approaches based on the consideration of minimum argument roots of edge and vertex polynomials are presented. For the computer-aided design of fractional order interval control systems, the minimum argument root principle is applied for a finite set of edge and vertex polynomials, which are sampled from parametric uncertainty box. Several illustrative examples are presented to discuss effectiveness of these approaches.

     

  • loading
  • [1]
    Bhattacharyya S P, Keel L H, Chapellat H. Robust Control:The Parametric Approach. Englewood Cliffs, NJ:Prentice Hall, 1995. 269-291 http://cn.bing.com/academic/profile?id=1574669531&encoded=0&v=paper_preview&mkt=zh-cn
    [2]
    Monje C A, Chen Y Q, Vinagre B M, Xue D Y, Feliu-Batlle V. Fractional-order Systems and Controls:Fundamentals and Applications. London:Springer, 2010.
    [3]
    Petráš I. Stability of fractional-order systems with rational orders:a survey. Fractional Calculus and Applied Analysis, 2009, 12(3):269-298 http://cn.bing.com/academic/profile?id=2481180091&encoded=0&v=paper_preview&mkt=zh-cn
    [4]
    Das S. Functional Fractional Calculus (Second edition). Berlin:Springer, 2011.
    [5]
    Chen Y Q, Ahn H S, Podlubny I. Robust stability check of fractional order linear time invariant systems with interval uncertainties. Signal Processing, 2006, 86(10):2611-2618 doi: 10.1016/j.sigpro.2006.02.011
    [6]
    Ahn H S, Chen Y Q, Podlubny I. Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality. Applied Mathematics and Computation, 2007, 187(1):27-34 doi: 10.1016/j.amc.2006.08.099
    [7]
    Ahn H S, Chen Y Q. Necessary and sufficient stability condition of fractional-order interval linear systems. Automatica, 2008, 44(11):2985-2988 doi: 10.1016/j.automatica.2008.07.003
    [8]
    Lu J G, Chen G R. Robust stability and stabilization of fractional-order interval systems:an LMI approach. IEEE Transactions on Automatic Control, 2009, 54(6):1294-1299 doi: 10.1109/TAC.2009.2013056
    [9]
    N'Doye I, Darouach M, Zasadzinski M, Radhy N E. Robust stabilization of uncertain descriptor fractional-order systems. Automatica, 2013, 49(6):1907-1913 doi: 10.1016/j.automatica.2013.02.066
    [10]
    Petráš I, Chen Y Q, Vinagre B M. A robust stability test procedure for a class of uncertain LTI fractional order systems. In:Proceedings of the 2002 International Carpathian Control Conference ICCC'2002. Malenovice, Czech Republic, 2002. 247-252
    [11]
    Petráš I, Chen Y Q, Vinagre B M. Robust stability test for interval fractional order linear systems. Unsolved Problems in Mathematical Systems and Control Theory. Princeton, NJ:Princeton University Press, 2004. 208-210
    [12]
    Lu J G, Chen Y Q. Robust stability and stabilization of fractional-order interval systems with the fractional order α:The 0 << α << 1 case. IEEE Transactions on Automatic Control, 2010, 55(1):152-158 doi: 10.1109/TAC.2009.2033738
    [13]
    Radwan A G, Soliman A M, Elwakil A S, Sedeek A. On the stability of linear systems with fractional-order elements. Chaos, Solitons and Fractals, 2009, 40(5):2317-2328 doi: 10.1016/j.chaos.2007.10.033
    [14]
    Senol B, Ates A, Alagoz B B, Yeroglu C. A numerical investigation for robust stability of fractional-order uncertain systems. ISA Transactions, 2014, 53(2):189-198 doi: 10.1016/j.isatra.2013.09.004
    [15]
    Matignon D. Stability results for fractional differential equations with applications to control processing. In:Proceedings of the 1996 Computational Engineering in Systems Applications. Lille, France, 1996. 963-968
    [16]
    Minnichelli R J, Anagnost J J, Desoer C A. An elementary proof of Kharitonov's stability theorem with extensions. IEEE Transactions on Automatic Control, 1989, 34(9):995-998 doi: 10.1109/9.35816
    [17]
    Podlubny I. Fractional Differential Equations. San Diego:Academic Press, 1999.
    [18]
    Xue D Y, Chen Y Q. Modeling, Analysis and Design of Control Systems in MATLAB and Simulink. River Edge, NJ, USA:World Scientific Publishing Company, 2014.
    [19]
    Caponetto R, Dongola G, Fortuna L, Petras I. Fractional Order Systems:Modeling and Control Applications. Singapore:World Scientific Publishing Company, 2010.
    [20]
    Sheil-Small T. Complex Polynomials. Cambridge, UK:Cambridge University Press, 2002.

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(10)  / Tables(2)

    Article Metrics

    Article views (1111) PDF downloads(7) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return