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

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2011)

  • Volume: 21, Issue: 3, page 521-524
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Tadeusz Kaczorek. "New stability conditions for positive continuous-discrete 2D linear systems." International Journal of Applied Mathematics and Computer Science 21.3 (2011): 521-524. <http://eudml.org/doc/208066>.

@article{TadeuszKaczorek2011,
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.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {positive systems; 2D linear systems; continuous-discrete systems},
language = {eng},
number = {3},
pages = {521-524},
title = {New stability conditions for positive continuous-discrete 2D linear systems},
url = {http://eudml.org/doc/208066},
volume = {21},
year = {2011},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - New stability conditions for positive continuous-discrete 2D linear systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2011
VL - 21
IS - 3
SP - 521
EP - 524
AB - 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.
LA - eng
KW - positive systems; 2D linear systems; continuous-discrete systems
UR - http://eudml.org/doc/208066
ER -

References

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  2. 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. 
  3. 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. Zbl1225.34020
  4. Busłowicz, M. (2011). Improved stability and robust stability conditions for a general model of scalar continuousdiscrete linear systems, Pomiary, Automatyka, Kontrola 57(2): 188-189. 
  5. Dymkov, M., Gaishun, I., Rogers, E., Gałkowski, K. and Owens, D.H. (2004). Control theory for a class of 2D continuousdiscrete linear systems, International Journal of Control 77 (9): 847-860. Zbl1060.93055
  6. Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
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  8. 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. Zbl1037.93050
  9. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
  10. Kaczorek, T. (2007). Positive 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 55(4): 351-358. 
  11. Kaczorek, T. (2008a). Positive fractional 2D hybrid linear systems, Bulletin of the Polish Academy of Sciences: Technical Sciences 56 (3): 273-277. 
  12. Kaczorek, T. (2008b). Realization problem for positive 2D hybrid systems, COMPEL 27 (3): 613-623. Zbl1148.93318
  13. 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. 
  14. 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. 
  15. Sajewski, Ł. (2009). Solution of 2D singular hybrid linear systems, Kybernetes 38 (7/8): 1079-1092. Zbl1325.93036
  16. 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. 
  17. 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. 
  18. 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. 

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