Computation of realizations of discrete-time cone-systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new notion of a realization of transfer matrix of (P, Q, V)-cone-system for discrete-time linear systems is proposed. Necessary and sufficient conditions for the existence of the realizations are established. A procedure is proposed for computation of a realization of a given proper transfer matrix T(z) of (P, Q, V)-cone-system. It is shown that there exists a realization of T(z) of (P, Q, V)-cone-system if and only if there exists a positive realization of T(z) = VT(Z)Q-1, where V, Q and P are non-singular matrices generating the cones V, Q and P respectively.

Słowa kluczowe

EN

computation; cone; positive realization; discrete-time system; procedure

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2006
• Tom: Vol. 54, nr 3
• Strony: 347--350
• Opis fizyczny: Bibliogr. 9 poz., 1 rys.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Bialystok Technical University, 45D Wiejska St., 15-351 Bialystok, Poland,

Bibliografia

• [1] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [2] T. Kaczorek, Positive 1D and 2D Systems, London: Springer-Verlag, 2002.
• [3] T. Kaczorek, “Some recent developments in positive systems”, Proc. 7th Conf. of Dynamical Systems Theory and Applications, pp. 25–35, Łódź, 2003.
• [4] M. Busłowicz, “Explicit solution of discrete-delay equations”, Foundations of Control Engineering 7 (2), 67–71 (1982).
• [5] L. Benvenuti and L. Farina, “A tutorial on the positive realization problem”, IEEE Trans. Autom. Control 49 (5), 651–664 (2004).
• [6] M. Busłowicz and T. Kaczorek, “Reachability and minimum energy control of positive linear discrete-time systems with one delay”, 12th Mediterranean Conference on Control and Automation, Kasadasi, Izmir, on CD, (2004).
• [7] G. Xie, and L. Wang, “Reachability and controllability of positive linear discrete-time systems with time-delays”, in Positive Systems, LNCIS 294, eds L. Benvenuti, A. De Santis, and L. Farina, Berlin: Springer-Verlag, 377–384 (2003).
• [8] T. Kaczorek, “Realization problem for positive discrete-time systems with delay”, System Science 30 (4), 117–130 (2004).
• [9] T. Kaczorek and M. Busłowicz, “Minimal realization for positive multivariable linear systems with delay”, Int. J. Appl. Math. Comput. Sci. 14 (2), 181–187 (2004).