Open Access

POSITIVE MINIMAL REALIZATION OF CONTINUOUS-DISCRETE LINEAR SYSTEMS WITH ALL-POLE AND ALL-ZERO TRANSFER FUNCTION


Cite

1. Antoniou G. E. (2002), Minimal state space realization for all-pole and all-zero lattice discrete 2D filters, International Journalof Systems Science, Vol. 33, No. 10, 799-803.Search in Google Scholar

2. Benvenuti L., Farina L. (2004), A tutorial on the positive realization problem, IEEE Trans. on Autom. Control, Vol. 49, No. 5, 651-664.Search in Google Scholar

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.Search in Google Scholar

4. Farina L., Rinaldi S. (2000), Positive Linear Systems; Theory andApplications, J. Wiley, New York.10.1002/9781118033029Search in Google Scholar

5. Kaczorek T. (1992), Linear control systems, Vol. 1, Research Studies Press J. Wiley, New York.Search in Google Scholar

6. Kaczorek T. (2002), Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2Search in Google Scholar

7. Kaczorek T. (2004), Realization problem for positive discrete-time systems with delay, System Science, Vol. 30, No. 4, 117-130.Search in Google Scholar

8. Kaczorek T. (2005), Positive minimal realizations for singular discrete-time systems with delays in state and delays in control, Bull.Pol. Acad. Sci. Tech., Vol. 53, No. 3, 293-298.Search in Google Scholar

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.Search in Google Scholar

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.Search in Google Scholar

11. Kaczorek T. (2007), Positive 2D hybrid linear systems, Bull. Pol.Acad. Sci. Tech., Vol. 55, No. 4,351-358.Search in Google Scholar

12. Kaczorek T. (2008a), Positive fractional 2D hybrid linear systems, Bull. Pol. Acad. Tech., Vol. 56, No. 3, 273-277.Search in Google Scholar

13. Kaczorek T. (2008b), Realization problem for positive 2D hybrid systems, COMPEL, Vol. 27, No. 3, 613-623.10.1108/03321640810861061Search in Google Scholar

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.Search in Google Scholar

15. Kaczorek T., Marchenko V., Sajewski Ł. (2008), Solvability of 2D hybrid linear systems - comparison of the different methods, ActaMechanica et Automatica, Vol. 2, No. 2, 59-66.Search in Google Scholar

16. Kurek J. (1985), The general state-space model for a twodimensional linear digital system, IEEE Trans. on Austom. Contr., AC-30, 600-602.10.1109/TAC.1985.1103998Search in Google Scholar

17. Roesser R. B. (1975), A discrete state-space model for linear image processing, IEEE Trans. on Autom. Contr., AC-20, 1-10.Search in Google Scholar

18. Sajewski Ł. (2009), Solution of 2D singular hybrid linear systems, Kybernetes, Vol. 38, No. 7/8, 2009, 1079-1092.Search in Google Scholar

19. Sajewski Ł., Kaczorek T. (2009), Computation of positive realizations of singular SISO hybrid linear systems, JAMRIS, Vol. 3, No. 4, 8-14.Search in Google Scholar

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.Search in Google Scholar

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 Models- Realization and the Notions of Controllability, Observability and Minimality, Proc. of the IEEE, Vol. 65, No. 6, 945-961.10.1109/PROC.1977.10592Search in Google Scholar

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.Search in Google Scholar