Positive different orders fractional 2D linear systems

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

A new class of positive different orders fractional 2D linear systems is introduced. A notion of (á, â) orders difference of 2D function is proposed. Fractional 2D state equations of linear systems are given and their solutions are derived using 2D Z-transform. The classical Cayley-Hamilton theorem is extended to the 2D fractional linear systems. Neccesary and sufficient conditions for the positivity, reachability and controllability to zero of the fractional 2D linear systems are established.

Słowa kluczowe

EN

linear systems; controllability

PL

systemy liniowe; sterowanie

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2008
• Tom: Vol. 2, no. 2
• Strony: 51--58
• Opis fizyczny: Bibliogr. 25 poz.

Twórcy

autor

Kaczorek T.

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

Bibliografia

• 1. Bose N.K (1982), Applied Multidimensional Systems Theory, Van Nonstrand Reinhold Co, New York.
• 2. Bose N.K (1985) Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reidel Publishing Co.
• 3. Farina L., Rinaldi S., (2000) Positive Linear Systems; Theory and Applications, J. Wiley, New York.
• 4. Fornasini E., Marchesini G., (1976) State-space realization theory of two-dimensional filters, IEEE Trans. Autom. Contr., Vol. AC-21, 484-491.
• 5. Fornasini E., Marchesini G. (1978) Double indexed dynamical systems, Math. Sys. Theory, 12, 59-72.
• 6. Gałkowski K. (1977), Elementary operation approach to state space realization of 2D systems, IEEE Trans. On Circuit and Systems, Vol. 44, 120-129.
• 7. Gałkowski K. (2001), State space realizations of linear 2D systems with extensions to the general nD (n>2) case, Springer Verlag, London.
• 8. Kaczorek T. (1985), Two-Dimensional Linear Systems, Springer Verlag, Berlin.
• 9. Kaczorek T. (2002) Positive 1D and 2D Systems, Springer Verlang, London.
• 10. Kaczorek T. (1996), Reachability and controllability of non-negative 2D Roesser type models, Bull. Acad. Pol. Sci. Ser. Sci. Techn., Vol. 44, No 4, 405-410
• 11. Kaczorek T. (2008) Realization problem of positive fractional 2D hybrid linear systems, COMPEL 2008, vol. 27, No. 3, 613-623.
• 12. Kaczorek T. (2007) Realization problem for positive 2D systems with delays. Machine Intelligence and Robotic Control, vol. 6, No. 1 (in Press).
• 13. Kaczorek T. (2005) Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics, vol. 34, No 2, 411-423.
• 14. Kaczorek T. (2007) Reachabilty and controllability to zero of positive fractional discrete-time systems. Machine Intelligence and Robotic Control, vol. 6, no. 2 (in Press).
• 15. Kaczorek T. (2008) Fractional positive continuous-time linear systems and their reachability. Int. J. Appl. Math. Comp. Sci., vol. 18, No. 2, 1-6.
• 16. Kaczorek T. (2003) Realization problem for positive discrete-time systems with delays, System Science, vol. 29, No 1,15-29.
• 17. Kaczorek T. (2005) Realization problem for a class of positive continuous-time systems with delays, Int. J. Appl. Math. Comp. Sci., vol. 15, No. 4, 101-107.
• 18. Kaczorek T. (2005) Realization problem for a class of positive continuous-time systems with delays, Int. J. Appl. Math Comput. Sci, vol. 15, No 4, 101-107.
• 19. Kaczorek T. (2008) Fractional 2D linear systems. Automation, Mobile Robotics and Intelligent Systems, vol. 2, no. 2, 1-6.
• 20. Kaczorek T. (2007) Reachability and controllability to zero of cone fractional linear systems. Archives of Control Scienes, vol. 17, No. 3, 357-367.
• 21. Kaczorek T., Busłowicz M. (2004) Minimal realization for positive multivariable linear systems with delay, Int. J. Appl. Math. Comput. Sci., vol. 14, No 2, 181-187.
• 22. Klamka J. (1991) Controllability of Dynamical Systems, Kluwer Academic Publ., Dordrecht, 1991.
• 23. Kurek J. (1985) The general state-space model for a two-dimensional linear digital systems, IEEE Trans. Autom. Contr. AC-30, 600-602.
• 24. Roesser R. P. (1975) A discrete state-space model for linear image processing, IEEE Trans. on Automatic Control, AC-20, 1, 1-10.
• 25. Valcher M. E. (1987) On the initial stability and asymptotic behavior of 2D positive systems, IEEE Trans. On Circuits and Systems – I, vol. 44, No 7, 602-613.