Positive switch 2D linear systems described by the general models

• Autorzy: Kaczorek T.
• Języki publikacji: EN

Abstrakty

EN

The positive switched 2D linear systems described by the general models are addressed. Necessary and sufficient conditions for the asymptotic stability of the positive switched system are established for any switching. The considerations are illustrated by numerical examples.

Słowa kluczowe

EN

asymptotic stability; positive 2D system; model

PL

stabilność praktyczna; dodatni układ dwuwymiarowy; model

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2010
• Tom: Vol. 4, no. 4
• Strony: 36--41
• Opis fizyczny: Bibliogr. 23 poz., rys.

Twórcy

autor

Kaczorek T.

• Białystok Technical University, Białystok,

Bibliografia

• 1. Bose N. K. (1985), Multidimensional Systems Theory Progress, Directions and Open Problems, D. Reidel Publishing Co..
• 2. Buslowicz M. (2008), Simple stability conditions for linear discrete-time systems with delays, Bull. Pol. Acad. Sci., Vol. 56, No. 4, 325-328.
• 3. Colaneri P. (2009), Dwell time analysis of deterministic and stochastic switched systems, European Journal of Control, 3-4, 228-248.
• 4. Farina L., Rinaldi S. (2000), Positive Linear Systems; Theory and Applications, J. Wiley, New York..
• 5. Fornasini E., Marchesini G. (1978), Double indexed dynamical systems, Math. Sys. Theory, 12:59-72.
• 6. Fornasini E., Marchesini G. (1976), State-space realization theory of two-dimensional filters, IEEE Trans, Autom. Contr., Vol. AC-21, 481-491.
• 7. Gałkowski K. (2001), State Space Realizations of Linear 2D Systems with Extensions to the General nD (n>2) Case, Springer -Verlag London.
• 8. Hu Q., Cheng D. (2008), Stabilizer design of planar switched linear systems, Systems& Control Letters, vol. 57, 876-879.
• 9. Kaczorek T. (2009), Asymptotic stability of positive 2D linear systems with delays, Bull. Pol. Acad. Sci. Techn., Vol. 27, No. 2, 133-138.
• 10. Kaczorek T. (2007), Choice of the forms of Lyapunov functions for positive 2D Roesser model, Int. J. Appl. Math. Comput. Sci., Vol. 17, No. 4, 471-475.
• 11. Kaczorek T. (2009), Independence of the asymptotic stability of positive 2D linear systems with delays of their delays, Int. J. Appl. Match. Comput. Sci., Vol. 19, No. 2, 255-261.
• 12. Kaczorek T. (2001), Positive 1D and 2D Systems, Springer -Verlag, London.
• 13. Kaczorek T. (1996), Reachability and controllability of nonnegative 2D Roesser type models, Bull. Acad. Pol. Sci. Techn., Vol. 44, No 4, 405-410.
• 14. Kaczorek T. (2005), Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics, vol. 34, No 2, 411-423.
• 15. Kaczorek T. (1985), Two-dimensional Linear Systems, Springer Verlag, Berlin.
• 16. Kaczorek T. (2002), When do equlibria of the positive 2D Roesser model are strictly positive, Bull. Acad. Pol. Sci. Techn., Vol. 50, No 1, 221-227.
• 17. Kurek J. (1985), The general state-space model for a twodimensional linear digital systems, IEEE Trans. Autom. Contr. AC-30, 600-602.
• 18. Liberzon D. (2009), On new sufficient conditions for stability of switched linear systems, Proc. European Control Conf., Budapest, 3257-3262.
• 19. Liberzon D. (2003), Switching in Systems and Control, Birkhoiser, Boston.
• 20. Otsuka N. (2010), Disturbance Decoupling Problems with Quadratic Stability for Switched Linear Systems via State Feedback, proceedings of MTNS’2010, Budapest, Hungary, 487-490.
• 21. Roesser R. P. (1975), A discrete state-space model for linear image processing, IEEE Trans. Autom. Contr., AC-20, 1,1-10.
• 22. Sun Z. D., Ge S. S. (2004), Switched Linear Systems: Control and Design, Springer.
• 23. Valcher M. E. (1997), On the internal stability and asymptotic behavior of 2D positive systems, IEEE Trans. On Circuits and Systems – I, vol. 44, No 7, 602-613.