New stability conditions for positive continuous-discrete 2D linear systems

Tadeusz Kaczorek

doi:10.2478/v10006-011-0040-z

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New stability conditions for positive continuous-discrete 2D linear systems

International Journal of Applied Mathematics and Computer Science

Volume 21 (2011): Issue 3 (September 2011)

By: Tadeusz Kaczorek

Open Access

|Sep 2011

Abstract

New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

References

Bistritz, Y. (2003). A stability test for continuous-discrete bivariate polynomials, Proceedings of the International Symposium on Circuits and Systems, Vol. 3, pp. 682-685.
Search in Google Scholar
Busłowicz, M. (2010a). Stability and robust stability conditions for a general model of scalar continuous-discrete linear systems, Pomiary, Automatyka, Kontrola 56(2): 133-135.10.2478/v10175-010-0056-9
Search in Google Scholar
Busłowicz, M. (2010b). Robust stability of the new general 2D model of a class of continuous-discrete linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 58(4): 561-566.10.2478/v10175-010-0056-9
Search in Google Scholar
Busłowicz, M. (2011). Improved stability and robust stability conditions for a general model of scalar continuous-discrete linear systems, Pomiary, Automatyka, Kontrola 57(2): 188-189.10.2478/v10175-010-0056-9
Search in Google Scholar
Dymkov, M., Gaishun, I., Rogers, E., Gałkowski, K. and Owens, D.H. (2004). Control theory for a class of 2D continuous-discrete linear systems, International Journal of Control 77 (9): 847-860.10.1080/00207170410001726796
Search in Google Scholar
Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, NewYork, NY.10.1002/9781118033029
Search in Google Scholar
Gałkowski, K., Rogers, E., Paszke, W. and Owens, D.H. (2003). Linear repetitive process control theory applied to a physical example, International Journal of Applied Mathematics and Computer Science 13 (1): 87-99.
Search in Google Scholar
Kaczorek, T. (1998). Reachability and minimum energy control of positive 2D continuous-discrete systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 46 (1): 85-93.
Search in Google Scholar
Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London.10.1007/978-1-4471-0221-2
Search in Google Scholar
Kaczorek, T. (2007). Positive 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(4): 351-358.
Search in Google Scholar
Kaczorek, T. (2008a). Positive fractional 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56 (3): 273-277.
Search in Google Scholar
Kaczorek, T. (2008b). Realization problem for positive 2D hybrid systems, COMPEL 27 (3): 613-623.10.1108/03321640810861061
Search in Google Scholar
Kaczorek, T. (2009). Stability of positive continuous-time linear systems with delays, Bulletin of the Polish Academy of Sciences: Technical Sciences 57(4): 395-398.10.2478/v10175-010-0143-y
Search in Google Scholar
Kaczorek, T., Marchenko, V. and Sajewski, Ł. (2008). Solvability of 2D hybrid linear systems—Comparison of the different methods, Acta Mechanica et Automatica 2(2): 59-66.
Search in Google Scholar
Sajewski, Ł. (2009). Solution of 2D singular hybrid linear systems, Kybernetes 38 (7/8): 1079-1092.10.1108/03684920910976835
Search in Google Scholar
Xiao, Y. (2001a). Stability test for 2-D continuous-discrete systems, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, Vol. 4, pp. 3649-3654.10.1109/CDC.2001.980427
Search in Google Scholar
Xiao, Y. (2001b). Robust Hurwitz-Schur stability conditions of polytopes of 2-D polynomials, Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, FL, USA, Vol. 4, pp. 3643-3648.10.1109/CDC.2001.980426
Search in Google Scholar
Xiao, Y. (2003). Stability, controllability and observability of 2-D continuous-discrete systems, Proceedings of the International Symposium on Circuits and Systems, Bangkok, Thailand, Vol. 4, pp. 468-471.
Search in Google Scholar