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Pointwise completeness and pointwise degeneracy of standard and positive fractional linear systems with state-feedbacks

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EN
Abstrakty
EN
The pointwise completeness and pointwise degeneracy of standard and positive fractional linear discrete-time and continuous-time systems with state-feedbacks are addressed. It is shown that the pointwise completeness and pointwise degeneracy of the fractional positive continuous-time systems are invariant under the state and output feedbacks. Necessary and sufficient conditions are established for the existence of gain matrices of state-feedbacks for standard and positive linear systems such that the closed-loop systems are pointwise complete. Considerations are illustrated by numerical examples.
Rocznik
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295--306
Opis fizyczny
Bibliogr. 16 poz.
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Bibliografia
  • [1] M. BUSŁOWICZ: Pointwise completeness and pointwise degeneracy of linear discrete-time systems of fractional order. Zesz. Nauk. Pol. Śląskiej, Automatyka, 151 (2008), 19-24 (in Polish).
  • [2] M. BUSŁOWICZ, R. KOCISZEWSKI and W. TRZASKO: Pointwise completeness and pointwise degeneracy of positive discrete-time systems with delays. Zesz. Nauk. Pol. Śląskiej, Automatyka, 145 (2006) 55-56 (in Polish).
  • [3] A. K. CHOUNDHURY: Necessary and sufficient conditions of pointwise completeness of linear time-invariant delay-differential systems. Int. J. Control, 16(6), (1972), 1083-1100.
  • [4] L. FARINA and S. RlNALDI: Positive linear systems; Theory and applications. J. Wiley, New York, 2000.
  • [5] T. KACZOREK: Positive ID and 2D Systems. Springer-Verlag, London, 2002.
  • [6] T. KACZOREK: Reachability and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, 6(4), (2008), 139-143.
  • [7] T. KACZOREK: Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comput. Sci., 18(2), (2008), 223-228.
  • [8] T. KACZOREK and M. BUSŁOWICZ: Pointwise completeness and pointwise degeneracy of linear continuous-time fractional order systems. Journal of Automation, Mobile Robotics & Intelligent Systems, 3(1), (2009), 8-11.
  • [9] T. KACZOREK: Pointwise completeness and pointwise degeneracy of standard and positive linear systems with state feedback. Przegląd Elektrotechniczny, (Electrical Review), 85(10), (2009).
  • [10] A. OLBROT: On degeneracy and related problems for linear constant time-lag systems. Ricerche di Automatica, 3(3), (1972), 203-220.
  • [11] P. OSTALCZYK: Epitome of the fractional calculus. Wydawnictwo Politechniki Łódzkiej, Łódź, 2008, (in Polish).
  • [12] I. PODLUBNY: Fractional differential eąuations. Academic Press, San Diego, 1999.
  • [13] V. M. POPOV: Pointwise degeneracy of linear time-invariant delay-differential equations. Journal ofDiff. Equation, 11 (1972), 541-561.
  • [14] J. SABATIER, O.P. AGRAWAL and J.A.T. MACHADO (EDS): Advances in fractional calculus, Theoretical developments and applications in physics and engineer-ing. Springer, London, 2007.
  • [15] W. TRZASKO, M. BUSŁOWICZ and T. KACZOREK: Pointwise completeness of discrete-time cone-systems with delays. Proc. EUROCON 2007, Warsaw, (2007), 606-611.
  • [16] L. WEISS: Controllability for various linear and nonlinear systems models. Lec-ture Notes in Mathematics, 144 Seminar on Differential Equations and Dynamie System II, Springer, Berlin, 1970, 250-262.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BSW3-0061-0016
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