Positive minimal realizations for singular discrete-time systems with delays in state and delays in control

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The positive (minimal) realization problem for a class of singular discrete-time linear single-input, single-output systems with delays in state and delays in control is addressed. Solvability conditions for the positive (minimal) realization problem are established. It is shown lat there exists a positive (minimal) realization of an improper transfer function T( z) = n( z) / d( z) if the coefficients of polynomial n( z) are on-negative and of the polynomial d( z) are non-positive except the leading one, which should be positive. A procedure for computation of le positive (minimal) realization of the transfer function is proposed and illustrated by an example.

Słowa kluczowe

EN

positive (minimal) realization; singular discrete-time systems; systems with delays, control

• Wydawca: Polska Akademia Nauk, Wydział IV Nauk Technicznych
• Czasopismo: Bulletin of the Polish Academy of Sciences. Technical Sciences
• Rocznik: 2005
• Tom: Vol. 53, nr 3
• Strony: 293--298
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Kaczorek T.

• Faculty of Electrical Engineering, Białystok Technical University 45D Wiejska 5tr., 15-351 Białystok.,

Bibliografia

• [1] H. Górecki, S. Fuksa, P. Grabowski, and A. Korytowski, Analysis and Synthesis of Time Delay Systems, PWN and J. Wiley, Warszawa 1989.
• [2] L. Farina and S. Rinaldi, Positive Linear Systems; Theory and Applications, J. Wiley, New York, 2000.
• [3] T. Kaczorek, Positive 1D and 2D Systems, Springer-Verlag, London 2002.
• [4] T. Kaczorek, “Some recent developments in positive systems”, Proc. 7th Conference of Dynamical Systems Theory and Applications, Łód´z, 25–35 (2003).
• [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, 2004.
• [7] 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).
• [8] T. Kaczorek and M. Busłowicz, “Reachability and minimum energy control of positive discrete-time linear systems with multiple delay in state and control”, (accepted for 44th IEEE CDC-ECC’05).
• [9] G. Xie and L. Wang, “Reachability and controllability of positive linear discrete-time systems with time-delays”, in: L. Benvenuti, A. De Santis and L. Farina (eds), Positive Systems LNCIS 294, pp. 377–384, Springer-Verlag, Berlin, 2003.
• [10] T. Kaczorek, “Realization problem for positive discrete-time systems with delay”, System Science 30(4), 2005 (to be published).
• [11] T. Kaczorek, “Realization problem for positive continuous-time systems with delays”, Proc. Intern. Conf. on Systems Engineering, Las Vegas, 2005.