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Stability of positive fractional switched continuous-time linear systems

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Języki publikacji
EN
Abstrakty
EN
The asymptotic stability of positive fractional switched continuous-time linear systems for any switching is addressed. Simple sufficient conditions for the asymptotic stability of the positive fractional systems are established. It is shown that the positive fractional switched systems are asymptotically stable for any switchings if the sum of entries of every column of the matrices of all subsystems is negative.
Rocznik
Strony
349--352
Opis fizyczny
Bibliogr. 24 poz., rys.
Twórcy
autor
  • Faculty of Electrical Engineering, Bialystok University of Technology, 45D Wiejska St., 15-351 Bialystok, Poland
Bibliografia
  • [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory andApplications, J. Wiley, New York, 2000.
  • [2] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London, 2002.
  • [3] M.D. Ortigueira, “Fractional discrete-time linear systems”, Proc. IEE-ICASSP 97 3, 2241-2244 (1997).
  • [4] I. Podlubny, Fractional Differential Equations, Academic Press, San Diego, 1999.
  • [5] T. Kaczorek, Selected Problems in Fractional Systems Theory, Springer-Verlag, Berlin, 2011.
  • [6] T. Kaczorek, “Positive switched 2D linear systems described by general model”, Acta Mechanica et Automatica 4, 36-41 (2010).
  • [7] T. Kaczorek, “Positive switched 2D linear systems described by the Roesser models”, Proc. 19th Int. Symp. Math. Theoryof Network and Systems 1, CD-ROM (2010).
  • [8] D. Liberzon, Switching in System and Control, Birklauser, Berlin, 2003.
  • [9] A. Benzaoui and, F. Tadeo, “Stabilization of positive switching linear discrete-time systems”, Int. J. Innovative Computing,Information and Control 6, 2427-2437 (2010).
  • [10] E. Fornasini and M.E. Valcher, “Stability and stabilizability criteria for discrete-time positive switched systems”, IEEE Trans. Autom. Control 57, 1208-1221 (2012).
  • [11] L. Gurvits, R. Shorten, and O. Mason, “On the stability of switched positive linear systems”, IEEE Trans. Autom. Control 52, 1099-1103 (2007).
  • [12] X.W. Liu, “Stability analysis of switched positive systems: a switched linear copositive Lyapunov function method”, IEEETrans. Circ. Sys. II, Express Brief 56, 414-418 (2009).
  • [13] X.W. Liu and C.Y. Dang, “Stability analysis of positive switched linear systems with delays”, IEEE Trans. Autom. Control 56, 1684-1690 (2011).
  • [14] X.W. Liu, L. Wang, W.S. Yu, and S.M. Zhong, “Constrained control of positive discrete-time systems with delays”, IEEETrans. Circ. Sys. II, Express Brief 55, 193-197 (2008).
  • [15] O. Mason and R. Shorten, “On linear copositive Lyapunov functions and the stability of switched positive linear systems”, IEEE Trans. Autom. Control 52, 1346-1349 (2007).
  • [16] X.D. Zhao, L.X. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching”, Automatica 48, 1132-1137 (2012).
  • [17] T. Kaczorek, “Choice of the forms of Lyapunov functions for 2D Roesser model”, Int. J. Apply. Math. and Comp. Sci. 17 (4), 71-475 (2007).
  • [18] S. Bundfuss and M. Dur, “Copositive Lyapunov functions for switched systems over cones”, System and Control Letters 58, 342-345 (2009).
  • [19] T. Kaczorek, “Simple sufficient conditions for asymptotic stability of positive linear systems for any switchings”, submitted to Bull. Pol. Ac.: Tech. 61 (2), 343-347 (2013).
  • [20] S. Hassan Hossein Nia, I. Tejado, and B.M. Vinagre, “Stability of fractional order switchin systems”, Proc. FDA’2012, FifthSymposium on Fractional Differentiation and its Applications 1, CD-ROM (2012).
  • [21] F.R. Gauntmacher, The Theory of Matrices, Chelses Publ. Comp., London, 1959.
  • [22] T. Kaczorek, Vectors and Matrices in Automation and Electrotechnics, WNT, Warszawa, 1998, (in Polish).
  • [23] T. Kaczorek, “Necessary and sufficient stability conditions of fractional positive continuous-time linear systems”, Acta Mechanicaet Automatica 5, 52-54 (2011).
  • [24] R.S. Varga, Matrix Interactive Analysis, Springer-Verlag, Berlin, 2002.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-92b35253-69a1-400b-bf70-7c681b3592dc
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