Independence of Asymptotic Stability of Positive 2D Linear Systems with Delays of Their Delays

Bose, N.K. (1982). Applied Multidimensional System Theory, Van Nostrand Reinhold Co., New York, NY.Search in Google Scholar

Bose, N.K. (1985). Multidimensional Systems Theory Progress: Directions and Open Problems, D. Reineld Publishing Co., Dordrecht.Search in Google Scholar

Busłowicz, M. (2007). Robust stability of positive discrete-time linear systems with multiple delays with linear unity rank uncertainty structure or non-negative perturbation matrices, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(1): 1-5.Search in Google Scholar

Busłowicz, M. (2008a). Robust stability of convex combination of two fractional degree characteristic polynomials, Acta Mechanica et Automatica 2(2): 5-10.Search in Google Scholar

Busłowicz, M. (2008b). Simple stability conditions for linear positive discrete-time systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(1): 325-328.Search in Google Scholar

Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY.10.1002/9781118033029Search in Google Scholar

Fornasini, E. and Marchesini, G. (1976). State-space realization theory of two-dimensional filters, IEEE Transactions on Automatic Control AC-21: 481-491.10.1109/TAC.1976.1101305Search in Google Scholar

Fornasini, E. and Marchesini, G. (1978). Double indexed dynamical systems, Mathematical Systems Theory 12: 59-72.10.1007/BF01776566Search in Google Scholar

Gałkowski, K. (1997). Elementary operation approach to state space realization of 2D systems, IEEE Transactions on Circuit and Systems 44: 120-129.10.1109/81.554329Search in Google Scholar

Gałkowski, K. (2001). State Space Realizations of Linear 2D Systems with Extensions to the General nD (n>2) Case, Springer-Verlag, London.Search in Google Scholar

Hmamed, A., Ait, Rami, M. and Alfidi, M. (2008). Controller synthesis for positive 2D systems described by the Roesser model, IEEE Transactions on Circuits and Systems, (submitted).10.1109/CDC.2008.4739294Search in Google Scholar

Kaczorek, T. (1985). Two-Dimensional Linear Systems, Springer-Verlag, Berlin.10.1007/BFb0005617Search in Google Scholar

Kaczorek, T. (2001). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2Search in Google Scholar

Kaczorek, T. (2009a). Asymptotic stability of positive 2D linear systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(1), (in press).10.2478/v10175-010-0113-4Search in Google Scholar

Kaczorek, T. (2009b). Asymptotic stability of positive 2D linear systems, Proceedings of the 14-th Scientific Conference on Computer Applications in Electrical Engineering, Poznań, Poland, pp. 1-11.Search in Google Scholar

Kaczorek, T. (2009c). LMI approach to stability of 2D positive systems, Multidimensional Systems and Signal Processing 20: 39-54.10.1007/s11045-008-0050-7Search in Google Scholar

Kaczorek, T. (2008a). Asymptotic stability of positive 1D and 2D linear systems, Recent Advances in Control and Automation, Academic Publishing House EXIT, pp. 41-52.Search in Google Scholar

Kaczorek, T. (2008c). Checking of the asymptotic stability of positive 2D linear systems with delays, Proceedings of the Conference on Computer Systems Aided Science and Engineering Work in Transport, Mechanics and Electrical Engineering, TransComp, Zakopane, Poland, Monograph No. 122, pp. 235-250, Technical University of Radom, Radom.Search in Google Scholar

Kaczorek, T. (2007). Choice of the forms of Lyapunov functions for positive 2D Roesser model, International Journal Applied Mathematics and Computer Science 17(4): 471-475.10.2478/v10006-007-0039-7Search in Google Scholar

Kaczorek, T. (2004). Realization problem for positive 2D systems with delays, Machine Intelligence and Robotic Control 6(2): 61-68.Search in Google Scholar

Kaczorek, T. (1996). Reachability and controllability of non-negative 2D Roesser type models, Bulletin of the Polish Academy of Sciences: Technical Sciences 44(4): 405-410.Search in Google Scholar

Kaczorek, T. (2005). Reachability and minimum energy control of positive 2D systems with delays, Control and Cybernetics 34(2): 411-423.Search in Google Scholar

Kaczorek, T. (2006a). Minimal positive realizations for discrete-time systems with state time-delays, International Journal for Computation and Mathematics in Electrical and Electronic Engineering, COMPEL 25(4): 812-826.10.1108/03321640610684015Search in Google Scholar

Kaczorek, T. (2006b). Positive 2D systems with delays, Proceedings of the 12-th IEEE/IFAC International Conference on Methods in Automation and Robotics, MMAR 2006, Międzyzdroje, Poland.Search in Google Scholar

Kaczorek, T. (2003). Realizations problem for positive discrete-time systems with delays, Systems Science 29(1): 15-29.Search in Google Scholar

Klamka, J. (1991). Controllability of Dynamical Systems, Kluwer Academic Publishers, Dordrecht.Search in Google Scholar

Kurek, J. (1985). The general state-space model for a two-dimensional linear digital systems, IEEE Transactions on Automatic Control AC-30: 600-602.10.1109/TAC.1985.1103998Search in Google Scholar

Roesser, R.P. (1975). A discrete state-space model for linear image processing, IEEE Transactions on Automatic Control AC-20(1): 1-1010.1109/TAC.1975.1100844Search in Google Scholar

Valcher, M.E. (1997). On the internal stability and asymptotic behavior of 2D positive systems, IEEE Transactions on Circuits and Systems—I 44(7): 602-613.10.1109/81.596941Search in Google Scholar