Positive 2D discrete-time linear Lyapunov systems

• Autorzy: Przemysław Przyborowski , Tadeusz Kaczorek
• Języki publikacji: EN

Abstrakty

EN

Two models of positive 2D discrete-time linear Lyapunov systems are introduced. For both the models necessary and sufficient conditions for positivity, asymptotic stability, reachability and observability are established. The discussion is illustrated with numerical examples.

Słowa kluczowe

EN

positivity; Lyapunov systems; reachability; observability

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2009
• Tom: 19
• Numer: 1
• Strony: 95-105

Daty

wydano

2009

otrzymano

2008-02-11

Twórcy

autor

Przemysław Przyborowski

• Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

autor

Tadeusz Kaczorek

• Institute of Control and Industrial Electronics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland

Bibliografia

• Bose, N.K. (1982). Applied Multidimensional System Theory, Van Nostrand Reinhold Co, New York, NY.
• Bose, N.K, Buchberger, B. and Guiver, J.P. (2003). Multidimensional Systems Theory and Applications, Kluwer Academic Publishers, Dordrecht.
• Busłowicz, M. (2006), Stability of positive linear discrete-time systems with unit delay with canonical forms of state matrices, Proceedings of 12-th IEEE International Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland.
• Farina, L. and Rinaldi, S. (2000). Positive Linear Systems Theory and Applications, Wiley, New York, NY.
• Fornasini, E. and Marchesini, G. (1976) State-space realization theory of two-dimensional filters, IEEE Transactions on Automatic Control 21(4): 481-491.
• Fornasini, E. and Marchesini, G. (1978). Double indexed dynamical systems, Mathematical Systems Theory 12: 59-72.
• Gałkowski, K. (2001). State Space Realizations of Linear 2D Systems with Extensions to the General nD (n > 2) Case, Springer, London.
• Kaczorek, T. (1985). Two-Dimensional Linear Systems, Springer, Berlin.
• Kaczorek, T. (1996). Reachability and controllability of nonnegative 2D Roesser type models, Bulletin of the Polish Academy of Sciences: Technical Sciences 44(4): 405-410.
• Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, Wydawnictwo Naukowo-Techniczne, Warsaw (in Polish).
• Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.
• Kaczorek, T. (2003). Realizations problem for positive discretetime systems with delays, Systems Science 29(1): 15-29.
• Kaczorek, T. (2004). Realization problem for positive 2D systems with delays, Machine Intelligence and Robotic Control 6(2): 61-68.
• Kaczorek, T. (2005). Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics 34(2): 411-423.
• Kaczorek, T. (2006a). Minimal positive realizations for discretetime systems with state time-delays, The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL 25(4): 812-826.
• Kaczorek, T. (2006b). Positive 2D systems with delays, Proceedings of the 12-th IEEE|IFAC International Conference on Methods in Automation and Robotics, Międzyzdroje, Poland.
• Kaczorek, T. (2007). Positive discrete-time linear Lyapunov systems, Proceedings of the 15-th Mediterranean Conference of Control and Automation, MED, Athens, Greece.
• Kaczorek, T. (2008a). Asymptotic stability of positive 2D linear systems, Proceedings of the 13-th Scientific Conference on Computer Applications in Electrical Engineering, Poznań, Poland.
• Kaczorek, T. (2008b). LMI approach to stability of 2D positive systems, Multidimensional Systems and Signal Processing, (in press).
• Kaczorek, T. (2008c). Asymptotic stability of positive 2D linear systems with delays, Lecture Notes in Electrical Engineering: Numerical Linear Algebra in Signals, Systems and Control, Springer-Verlag.
• Kaczorek, T. and Przyborowski, P. (2007a). Positive continuoustime linear Lyapunov systems, Proceedings of the International Conference on Computer as a Tool, EUROCON 2007, Warsaw, Poland, pp. 731-737.
• Kaczorek, T. and Przyborowski, P. (2007b). Positive continuoustime linear time-varying Lyapunov systems, Proceedings of the 16-th International Conference on Systems Science, Wrocław, Poland, Vol. I, pp. 140-149.
• Kaczorek, T. and Przyborowski, P. (2007c). Continuoustime linear Lyapunov cone-systems, Proceedings of the 13-th IEEE IFAC International Conference on Methods and Models in Automation and Robotics, Szczecin, Poland, pp. 225-229.
• Kaczorek, T. and Przyborowski, P. (2007d). Positive discretetime linear Lyapunov systems with delays, Przegląd Elektrotechniczny (2): 12-15.
• Kaczorek, T. and Przyborowski, P. (2007e). Positive linear Lyapunov systems, FNA-ANS International Journal - Problems of Nonlinear Analysis in Engineering Systems 13(2): 35-60.
• Kaczorek, T. and Przyborowski, P. (2008). Reachability, controllability to zero and observability of the positive discretetime Lyapunov systems, Control and Cybernetics Journal, (submitted).
• Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer, Dordrecht.
• Klamka, J. (1996a). Controllability of 2-D systems, Proceedings of the 3-rd Conference on Methods and Models in Automation and Robotics, Międzyzdroje, Poland, pp. 207-212.
• Klamka, J. (1996b). Controllability and minimum energy control of 2-D linear systems, Proceedings of the International Conference on Circuits Systems and Computers, Athens, Greece, Vol. 1, pp. 45-50.
• Klamka, J. (1997a). Controllability of infinite-dimensional 2-D linear systems, Advances in Systems Science and Applications 1(1): 537-543.
• Klamka, J. (1997b). Controllability of nonlinear 2-D systems, Nonlinear Analysis, Theory, Methods and Applications 30(5): 2963-2968.
• Klamka, J. (1997c). Controllability of 2-D systems systems: A survey, Applied Mathematics and Computer Science 7(4): 101-120.
• Klamka, J. (1997d). Controllability and minimum energy control of 2-D linear systems, Proceedings of the American Control Conference ACC'97, Albuquerque, NM, USA, Vol. 5, pp. 3141-3143.
• Klamka, J. (1998a). Constrained controllability of positive 2-D systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 46(1): 95-104.
• Klamka, J. (1998b). Constrained controllability of 2-D systems, Proceedings of the Symposium on Modelling Analysis and Control, Hammamet, Tunisia.
• Klamka, J. (1998c). Constrained controllability of linear positive 2-D systems, Proceedings of the 9-th Symposium on Systems, Modelling, Control, SMC-9, Zakopane, Poland.
• Klamka, J. (1999a). Local controllability of 2-D nonlinear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 47(2): 153-161.
• Klamka, J. (1999b). Controllability of 2-D linear systems, in P.M. Frank (Ed.), Advances in Control. Highlights of ECC'99, Springer, Berlin, pp. 319-326.
• Klamka, J. (1999c). Controllability of 2-D nonlinear systems, Proceedings of the European Control Conference, Karlsruhe, Germany, pp. 1121-1127.
• Klamka, J. (2002). Positive controllability of positive dynamical systems, Proceedings of the American Control Conference, Anchorage, AK, USA, (on CD-ROM).
• Klamka, J. (2005). Approximate constrained controllability of mechanical systems, Journal of Theoretical and Applied Mechanics 43(3): 539-554.
• Kurek, J. (1985). The general state-space model for a twodimensional linear digital systems, IEEE Transactions on Automatic Control 30(6): 600-602.
• Murty, M.S.N. and Apparao, B.V. (2005). Controllability and observability of Lyapunov systems, Ranchi University Mathematical Journal 32: 55-65.
• Przyborowski, P. (2008a). Positive fractional discrete-time Lyapunov systems, Archives of Control Sciences 18(LIV)(1): 5-18.
• Przyborowski, P. (2008b). Fractional discrete-time Lyapunov cone-systems, Przegląd Elektrotechniczny (5): 47-52.
• Przyborowski, P. and Kaczorek, T. (2008). Linear Lyapunov cone-systems, in J. M. Ramos Arreguin (Ed.), Automation and Robotics-New Challenges, I-Tech Education and Publishing, Vienna, (in press).
• Roesser, R.P. (1975). A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control 20(1): 1-10.
• Twardy, M. (2007). An LMI approach to checking stability of 2D positive system, Bulletin of the Polish Academy of Sciences: Technical Sciences 54(4): 385-395
• Valcher, M.E. (1997). On the internal stability and asymptotic behavior of 2D positive systems, IEEE Transactions On Circuits and Systems-I 44(7): 602-613.

Identyfikatory

DOI

10.2478/v10006-009-0009-3