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2013 | 42 | nr 2 | 315--327
Tytuł artykułu

Positive Realizations on Time Scales

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The problem of realization of a linear input-output map as a positive linear system on a time scale is studied. To state the criteria of existence of realization, modified Markov parameters corresponding to the input-output map are introduced. It is necessary for the existence of a positive realization that the modified Markov parameters be nonnegative. A necessary and sufficient condition for realizability is expressed in the language of positive cones in an infinite dimensional space. The sequence of modified Markov parameters generates one of the cones that appear in the criterion of realizability. (original abstract)
Rocznik
Tom
42
Numer
Strony
315--327
Opis fizyczny
Twórcy
  • Bialystok University of Technology, Poland
Bibliografia
  • Anderson, B.D.O., Deistler, M., Farina, L. and Benvenuti, L. (1996) Nonnegative realization of a linear system with nonnegative impulse response. IEEE Transactions on Circuits and Systems CAS-43, 134-142.
  • Bartosiewicz, Z. (2012) Observability of linear positive systems on time scales. Proceedings of the 51st IEEE Conference on Decision and Control, Maui, Hawaii, December 10-13, 2012. IEEE, 2581-2586.
  • Bartosiewicz, Z. (2013) Linear positive control systems on time scales; controllability. Mathematics of Control, Signals, and Systems DOI 10.1007/s00498-013-0106-6
  • Bartosiewicz, Z. and Pawluszewicz, E. (2006) Realizations of linear control systems on time scales. Control Cybernet., 35, 769-786.
  • Bohner, M. and Guseinov, G. Sh. (2007) The Convolution on Time Scales. Abstract and Applied Analysis, Article ID 58373. doi:10.1155/2007/58373
  • Bohner, M. and Peterson, A. (2001) Dynamic Equations on Time Scales. Birkhäuser, Boston.
  • Bru, R., Romero, S. and Sanchez, E. (2000) Canonical forms for positive discrete-time linear control systems. Linear Algebra Appl. 310, 49-71.
  • Commault, Ch. (2004) A simple graph theoretic characterization of reachability for positive linear systems. Syst. Control Lett. 52, 275-282.
  • Commault, Ch. and Alamir, M. (2007) On the reachability in any fixe time for positive continuous-time linear systems. Syst. Control Lett. 56, 272-276.
  • Coxson, P.G. and Shapiro, H. (1987) Positive reachability and controllability of positive systems. Lin. Alg. Appl. 94, 35-53.
  • Damm, T. and Ethington, C. (2009) Detectability, observability, and asymptotic reconstructability of positive systems. In: R. Bru, S. Romero-Vivó, eds., Positive Systems, Springer, New York.
  • Fanti, M., Maione, B. and Turchiano, B. (1990) Controllability of multiinput positive discrete-time systems. Int. J. Control 51, 1295-1308.
  • Farina, L. (1995) Necessary conditions of positive realizability for continuoustime linear systems. Syst. Control Lett. 25, 21-24.
  • Farina, L. (1996) On the existence of a positive realization. Syst. Control Lett. 28, 219-226.
  • Farina, L. and Rinaldi, S. (2000) Positive Linear Systems: Theory and Applications. Pure and Applied Mathematics, JohnWiley & Sons, New York.
  • Kaczorek, T. (2002) Positive 1D and 2D Systems. Springer-Verlag, London.
  • Kaczorek, T. (2007) New reachability and observability tests for positive linear discrete-time systems. Bull. Pol. Acad. Sci., Technical Sciences 55, 19-21.
  • Maeda, H. and Kodama, S. (1981) Positive realizations of difference equations. IEEE Trans. Circuits and Systems 28, 39-47.
  • Ohta, Y., Maeda, H. and Kodama, S. (1984) Reachability, observability and realizability of continuous positive systems. SIAM J. Control Optim. 22, 171-180.
  • Valcher, M.E. (1996) Controllability and reachability criteria for discrete time positive systems. Int. J. of Control 65, 511-536.
  • Valcher, M.E. (2009) Reachability properties for continuous-time positive systems. IEEE Trans. Automat. Control 54, 1586-1590.
  • van den Hof, J.M. (1987) Realization of positive linear systems. Linear Algebra and Its Applications 256, 287-308.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.ekon-element-000171304009

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