Positive Minimal Realization of Continuous-Discrete Linear Systems with All-Pole and All-Zero Transfer Function

• Autorzy: Sajewski Ł.
• Języki publikacji: EN

Abstrakty

EN

The positive and minimal realization problem for continuous-discrete linear single-input and single-outputs (SISO) systems is formulated. Two special case of the continuous-discrete systems are given. Method based on the state variable diagram for finding a positive and minimal realization of a given proper transfer function is proposed. Sufficient conditions for the existence of a positive minimal realization of a given proper transfer function of all-pole and all-zero systems are established. Two procedures for computation of a positive minimal realization are proposed and illustrated by a numerical examples.

Słowa kluczowe

EN

continous-discrete; 2D problems; minimal; positive; realization; existence; computation

PL

zagadnienia 2D; realizacja dodatnia; obliczanie

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2013
• Tom: Vol. 7, no. 1
• Strony: 42--47
• Opis fizyczny: Bibliogr. 22 poz., wykr.

Twórcy

autor

Sajewski Ł.

• Faculty of Electrical Engineering, Bialystok University of Technology, ul. Wiejska 45c, 15-351 Białystok, Poland,

Bibliografia

• 1. Antoniou G. E. (2002), Minimal state space realization for all-pole and all-zero lattice discrete 2D filters, International Journal of Systems Science, Vol. 33, No. 10, 799-803.
• 2. Benvenuti L., Farina L. (2004), A tutorial on the positive realization problem, IEEE Trans. on Autom. Control, Vol. 49, No. 5, 651-664.
• 3. Dymkov M., Gaishun I., Rogers E., Gałkowski K., Owens D. H.(2004), Control theory for a class of 2D continuous-discrete linear systems, Int. J. Control Vol. 77, No. 9, 847-860.
• 4. Farina L., Rinaldi S. (2000), Positive Linear Systems; Theory and Applications, J. Wiley, New York.
• 5. Kaczorek T. (1992), Linear control systems, Vol. 1, Research Studies Press J. Wiley, New York.
• 6. Kaczorek T. (2002), Positive 1D and 2D Systems, Springer-Verlag, London.
• 7. Kaczorek T. (2004), Realization problem for positive discrete-time systems with delay, System Science, Vol. 30, No. 4, 117-130.
• 8. Kaczorek T. (2005), Positive minimal realizations for singulardiscrete-time systems with delays in state and delays in control, Bull. Pol. Acad. Sci. Tech., Vol. 53, No. 3, 293-298.
• 9. Kaczorek T. (2006a), A realization problem for positive continuoustime linear systems with reduced numbers of delay, Int. J. Appl. Math. Comp. Sci., Vol. 16, No. 3, 325-331.
• 10. Kaczorek T. (2006b), Realization problem for positive multivariable discrete-time linear systems with delays in the state vector and inputs, Int. J. Appl. Math. Comp. Sci., Vol. 16, No. 2, 101-106.
• 11. Kaczorek T. (2007), Positive 2D hybrid linear systems, Bull. Pol. Acad. Sci. Tech., Vol. 55, No. 4,351-358.
• 12. Kaczorek T. (2008a), Positive fractional 2D hybrid linear systems, Bull. Pol. Acad. Tech., Vol. 56, No. 3, 273-277.
• 13. Kaczorek T. (2008b), Realization problem for positive 2D hybrid systems, COMPEL, Vol. 27, No. 3, 613-623.
• 14. Kaczorek T., Busłowicz M. (2004), Minimal realization problem for positive multivariable linear systems with delay, Int. J. Appl. Math. Comput. Sci., Vol. 14, No. 2, 181-187.
• 15. Kaczorek T., Marchenko V., Sajewski Ł. (2008), Solvability of 2D hybrid linear systems - comparison of the different methods, Acta Mechanica et Automatica, Vol. 2, No. 2, 59-66.
• 16. Kurek J. (1985), The general state-space model for a twodimensional linear digital system, IEEE Trans. on Austom. Contr., AC-30, 600-602.
• 17. Roesser R. B. (1975), A discrete state-space model for linear image processing, IEEE Trans. on Autom. Contr., AC-20, 1-10.
• 18. Sajewski Ł. (2009), Solution of 2D singular hybrid linear systems, Kybernetes, Vol. 38, No. 7/8, 2009, 1079-1092.
• 19. Sajewski Ł., Kaczorek T. (2009), Computation of positive realizations of singular SISO hybrid linear systems, JAMRIS, Vol. 3, No. 4, 8-14.
• 20. Sajewski Ł., Kaczorek T. (2010), Computation of positive realizations of MIMO hybrid linear systems in the form of second Fornasini-Marchesini model, Archives of Control Sciences, Vol. 20, No. 3, 253-271.
• 21. Sun-Yuan Kung, Levy B.C., Morf M., Kailath T. (1977), New Results in 2-D Systems Theory, Part II: 2-D State-Space ModelsRealization and the Notions of Controllability, Observability and Minimality, Proc. of the IEEE, Vol. 65, No. 6, 945-961.
• 22. Varoufakis S. J., Paraskevopoulos P.N., Antoniou G. E. (1987), On the minimal state-space realizations of all-pole and all-zero 2-D systems, IEEE Trans. on Circ. and Sys., Vol. 34, No. 3, 289-292.