Geodesic
Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs
International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 2, pp. 169-174.

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The realization problem for positive multivariable discrete-time systems with delays in the state and inputs is formulated and solved. Conditions for its solvability and the existence of a minimal positive realization are established. A procedure for the computation of a positive realization of a proper rational matrix is presented and illustrated with examples.
Keywords: positive realization, discrete-time system, time delay, existence, computation
Mots-clés : realizacja dodatnia, układ dyskretno czasowy, opóźnienie czasowe, obliczanie 
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Kaczorek, T. Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs. International Journal of Applied Mathematics and Computer Science, Tome 16 (2006) no. 2, pp. 169-174. http://geodesic.mathdoc.fr/item/IJAMCS_2006_16_2_a0/

[1] Benvenuti L. and Farina L. (2004): A tutorial on the positive realization problem. - IEEE Trans. Automat. Contr., Vol. 49, No. 5, pp. 651-664.

[2] Busłowicz M. (1982): Explicit solution of discrete-delay equations. - Found. Contr. Eng., Vol. 7, No. 2, pp. 67-71.

[3] Busłowicz M. and Kaczorek T. (2004): Reachability and minimum energy control of positive linear discrete-time systems with one delay. - Proc. 12th Mediterranean Conference Control and Automation, Kasadasi, Izmir, Turkey, (on CDROM).

[4] Farina L. and Rinaldi S. (2000): Positive Linear Systems - Theory and Applications. -New York: Wiley.

[5] Kaczorek T. (2002): Positive 1D and 2D Systems. - London: Springer.

[6] Kaczorek T. (2003): Some recent developments in positive systems. - Proc. 7-th Conf. Dynamical Systems Theory and Applications, Łód´z, Poland, pp. 25-35.

[7] Kaczorek T. (2004): Realization problem for positive discretetime systems with delay. - Syst. Sci., Vol. 30, No. 4, pp. 117-130.

[8] Kaczorek T. (2005): Realization problem for positive continuous-time systems with delays. - Proc. Int. Conf. Systems Engineering, Las Vegas, USA, (on CD-ROM).

[9] Kaczorek T. and Busłowicz M. (2004): Minimal realization for positive multivariable linear systems with delay. - Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 2, pp. 181-187.

[10] Klamka J. (1991): Controllability of Dynamical Systems. - Dordrecht: Kluwer.

[11] Xie G. and Wang L. (2003): Reachability and controllability of positive linear discrete-time systems with time-delays, In: Positive Systems (L. Benvenuti, A. De Santis and L. Farina, Eds.).-Berlin: Springer, pp. 377-384.