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On positive reachability of time-variant linear systems on time scales

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Języki publikacji
EN
Abstrakty
EN
Positive reachability of time-variant linear positive systems on arbitrary time scales is studied. It is shown that the system is positively reachable if and only if a modified Gram matrix corresponding to the system is monomial. The general criterion is then specified for particular cases of continuous-time systems and various classes of discrete-time systems. It is shown that in the case of continuous-time systems with analytic coefficients the conditions for positive reachability are very restrictive, similarly as for time-invariant systems.
Twórcy
  • Bialystok University of Technology, 45A Wiejska St., 15-351 Białystok, Poland
Bibliografia
  • [1] L. Farina and S. Rinaldi, Positive Linear Systems: Theory and Applications, Pure and Applied Mathematics, John Wiley & Sons, New York, 2000.
  • [2] T. Kaczorek, Positive 1D and 2D Systems. Springer-Verlag, London, 2002.
  • [3] Y. Ohta, H. Maeda, and S. Kodama, “Reachability, observability and realizability of continuous-time positive systems”, SIAM J. Control Optim. 22, 171-180 (1984).
  • [4] V.G. Rumchev and D.J.G. James, “Controllability of positive discrete-time systems”, Int. J. Control 50, 845-857 (1989).
  • [5] P.G. Coxson and H. Shapiro, “Positive input reachability and controllability of positive linear systems”, Linear Algebra Appl. 94, 35-53 (1987).
  • [6] M. Fanti, B. Maione, and B. Turchiano, “Controllability of multiinput positive discrete-time systems”, Int. J. Control 51, 1295-1308 (1990).
  • [7] T. Kaczorek, “New reachability and observability tests for positive linear discrete-time systems”, Bull. Pol. Ac.: Tech. 55, 19-21 (2007).
  • [8] R. Bru, S. Romero, and E. Sanchez, “Canonical forms for positive discrete-time linear control systems”, Linear Algebra Appl. 310, 49-71 (2000).
  • [9] Ch. Commault, “A simple graph theoretic characterization of reachability for positive linear systems”, Syst. Control Lett. 52, 275-282 (2004).
  • [10] Ch. Commault and M. Alamir, “On the reachability in any fixed time for positive continuous-time linear systems”, Syst. Control Lett. 56, 272-276 (2007).
  • [11] M.E. Valcher, “Reachability properties for continuous-time positive systems”, IEEE Trans. Automat. Control 54, 1586-1590 (2009).
  • [12] T. Kaczorek, “Fractional positive continuous-time linear systems and their reachability”, Int. J. Appl. Math. Comput. Sci. 18 (2), 223-228 (2008).
  • [13] T. Kaczorek, “Positive fractional 2D continuous-discrete linear systems”, Bull. Pol. Ac: Tech. 59 (4), 575-579 (2011).
  • [14] T. Kaczorek, “Positive fractional continuous-time linear systems with singular pencils”, Bull. Pol. Ac: Tech. 60 (1), 9-12 (2012).
  • [15] Z. Bartosiewicz, “Linear positive control systems on time scales; controllability”, Math. Control Signals Syst. 25 (3), 327-349 (2013).
  • [16] Z. Bartosiewicz, “Observability of linear positive systems on time scales”, Proc. 51st IEEE Conf. on Decision and Control 1, 2581-2586 (2012).
  • [17] Z. Bartosiewicz and E. Pawłuszewicz, “Unification of continuous-time and discrete-time systems: the linear case”, Proc. Sixteenth Int. Symp. on Mathematical Theory of Networks and Systems (MTNS2004) 1, 5-9 (2004).
  • [18] Z. Bartosiewicz and E. Pawłuszewicz, “Realizations of linear control systems on time scales”, Control Cybernet. 35, 769-786 (2006).
  • [19] Z. Bartosiewicz, “Positive realizations on time scales”, Control Cybernet. 42 (2), 315-327 (2013).
  • [20] M. Bohner and A. Peterson, Dynamic Equations on Time Scales, Birkh¨auser, Boston, 2001.
  • [21] G.Sh. Guseinov, “Integration on Time Scales”, J. Math. Anal.Appl. 285, 107-127 (2003).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-e113a665-f799-426e-b414-ef3d3ea43044
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