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Fractional Calculus and Applied Analysis

Editor-in-Chief: Kiryakova, Virginia


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Volume 19, Issue 3

Issues

Perfect nonlinear observers of fractional descriptor continuous-time nonlinear systems

Tadeusz Kaczorek
Published Online: 2016-06-23 | DOI: https://doi.org/10.1515/fca-2016-0041

Abstract

Perfect nonlinear fractional descriptor observers for fractional descriptor continuous-time nonlinear systems are proposed. Necessary and sufficient conditions for the existence of the observers are established. The design procedure of the nonlinear fractional observers is given. It is based on the elementary row (column) operations and reducing the singular matrix of the system to upper (lower) triangular form. The effectiveness of the procedure is demonstrated on a numerical example.

Key Words and Phrases: fractional descriptor nonlinear systems; design; perfect; descriptor; fractional; observer

MSC 2010: Primary 34K37; Secondary: 93C10, 93C35, 93C41

References

  • [1]

    Cuihong W. New delay-dependent stability criteria for descriptor systems with interval time delay Asian Journal of Control 14 No 1 2012 197 206 DOI: CrossrefGoogle Scholar

  • [2]

    Dai L. Singular Control Systems, Lecture Notes in Control and Information Sciences Springer-Verlag Berlin 1989 DOI: CrossrefGoogle Scholar

  • [3]

    Dodig M. Stosic M. Singular systems, state feedbacks problem Linear Algebra and its Applications 431 No 8 2009 1267 1292 DOI: CrossrefGoogle Scholar

  • [4]

    Duan G. Analysis and Design of Descriptor Linear Systems Springer-Verlag New York 2010 DOI: CrossrefGoogle Scholar

  • [5]

    Fahmy M.M. O’Reilly J. Matrix pencil of closed-loop descriptor systems: infinite-eigenvalue assignment Int. J. Control 49 No 4 1989 1421 1431 DOI: CrossrefGoogle Scholar

  • [6]

    Gantmacher F.R. The Theory of Matrices Chelsea Publishing Co. New York 1960Google Scholar

  • [7]

    Kaczorek T. Checking of the positivity of descriptor linear systems with singular pencils Archives of Control Sciences 22 No 1 2012 77 86 DOI: CrossrefGoogle Scholar

  • [8]

    Kaczorek T. Descriptor fractional linear systems with regular pencils Asian Journal of Control 15 No 4 2013 1051 1064; DOI: CrossrefGoogle Scholar

  • [9]

    Kaczorek T. Fractional descriptor observers for fractional descriptor continuous-time linear system Archives of Control Sciences 24 No 1 2014 39 5 2 DOI: CrossrefGoogle Scholar

  • [10]

    Kaczorek T. Fractional positive continuous-time linear systems and their reachability Int. J. Appl. Math. Comput. Sci. 18 No 2 2008233-228; DOI: CrossrefWeb of ScienceGoogle Scholar

  • [11]

    Kaczorek T. Full-order perfect observers for continuous-time linear systems Bull. Pol. Acad. Sci.: Tech. 49 No 4 2001 549 558Google Scholar

  • [12]

    Kaczorek T. Infinite eigenvalue assignment by an output feedback for singular systems Int. J. Appl. Math. Comput. Sci. 14 No 1 2004 19 23 DOI: CrossrefGoogle Scholar

  • [13]

    Kaczorek T. Linear Control Systems: Analysis of Multivariable Systems J. Wiley & Sons New York 1992Google Scholar

  • [14]

    Kaczorek T. Perfect observers of fractional descriptor continuous-time linear system In: Advances in Modelling and Control of Non-integer Order Systems 320 2015 3 12 Springer DOI: CrossrefGoogle Scholar

  • [15]

    Kaczorek T. Positive fractional continuous-time linear systems with singular pencils Bull. Pol. Ac.: Tech. 60 No 1 2012 9 12 DOI: CrossrefWeb of ScienceGoogle Scholar

  • [16]

    Kaczorek T. Positive linear systems consisting of n subsystems with different fractional orders IEEE Trans. on Circuits and Systems 58 No 6 2011 1203 1210 DOI: CrossrefWeb of ScienceGoogle Scholar

  • [17]

    Kaczorek T. Reduced-order fractional descriptor observers for fractional descriptor continuous-time linear system Bull. Pol. Acad. Sci.: Tech. 62 No 4 2014 889 895 DOI: CrossrefGoogle Scholar

  • [18]

    Kaczorek T. Selected Problems of Fractional Systems Theory Springer-Verlag Berlin 2011 DOI: CrossrefGoogle Scholar

  • [19]

    Kociszewski R. Observer synthesis for linear discrete-time systems with different fractional orders Measurements Automation Robotics (PAR) 17 No 2 2013 376 381(in Polish, CD-ROM)Google Scholar

  • [20]

    Kucera V. Zagalak P. Fundamental theorem of state feedback for singular systems Automatica 24 No 5 1988 653 658 DOI: CrossrefGoogle Scholar

  • [21]

    Lewis F.L. Descriptor systems: Expanded descriptor equation and Markov parameters IEEE Trans. Autom. Contr. 28 No 5 1983 623 627 DOI: CrossrefGoogle Scholar

  • [22]

    Luenberger D.G. Dynamic equations in descriptor form IEEE Trans. Autom. Contr. 22 No 3 1977 312 321 DOI: CrossrefGoogle Scholar

  • [23]

    Luenberger D.G. Time-invariant descriptor systems Automatica 14 No 5 1978 473 480 DOI: CrossrefGoogle Scholar

  • [24]

    N’Doye I. Darouach M. Voos H. Zasadzinski M. Design of unknown input fractional-order observers for fractional-order systems Int. J. Appl. Math. Comput. Sci. 23 No 3 2013 491 500 DOI: CrossrefWeb of ScienceGoogle Scholar

  • [25]

    Podlubny I. Fractional Differential Equations Academic Press New York 1999Google Scholar

  • [26]

    Van Dooren P. The computation of Kronecker's canonical form of a singular pencil Linear Algebra and its Applications 24 1979 103 140 DOI: CrossrefGoogle Scholar

  • [27]

    Virnik E. Stability analysis of positive descriptor systems Linear Algebra and its Applications 429 No 10 2008 2640 2659 DOI: CrossrefGoogle Scholar

About the article

Received: 2015-06-01

Revised: 2016-02-07

Published Online: 2016-06-23

Published in Print: 2016-06-01


Citation Information: Fractional Calculus and Applied Analysis, Volume 19, Issue 3, Pages 775–784, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2016-0041.

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