Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems

Tadeusz Kaczorek

International Journal of Applied Mathematics and Computer Science (2013)

  • Volume: 23, Issue: 3, page 501-506
  • ISSN: 1641-876X

Abstract

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Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.

How to cite

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Tadeusz Kaczorek. "Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems." International Journal of Applied Mathematics and Computer Science 23.3 (2013): 501-506. <http://eudml.org/doc/262485>.

@article{TadeuszKaczorek2013,
abstract = {Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.},
author = {Tadeusz Kaczorek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {Padé approximation; fractional system; linear positive system},
language = {eng},
number = {3},
pages = {501-506},
title = {Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems},
url = {http://eudml.org/doc/262485},
volume = {23},
year = {2013},
}

TY - JOUR
AU - Tadeusz Kaczorek
TI - Approximation of fractional positive stable continuous-time linear systems by fractional positive stable discrete-time systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2013
VL - 23
IS - 3
SP - 501
EP - 506
AB - Fractional positive asymptotically stable continuous-time linear systems are approximated by fractional positive asymptotically stable discrete-time systems using a linear Padé-type approximation. It is shown that the approximation preserves the positivity and asymptotic stability of the systems. An optional system approximation is also discussed.
LA - eng
KW - Padé approximation; fractional system; linear positive system
UR - http://eudml.org/doc/262485
ER -

References

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  4. Busłowicz, M. and Kaczorek, T. (2009). Simple conditions for practical stability of positive fractional discrete-time linear systems, International Journal of Applied Mathematics and Computer Science 19(2): 263-269, DOI: 10.2478/v10006-009-0022-6. Zbl1167.93019
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  7. Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
  8. Kaczorek, T. (1999). Relationship between the value of discretisation step and positivity and stabilization of linear dynamic systems, Proceedings of the Conference on Simulation, Designing and Control of Foundry Processes, Kraków, Poland, pp. 33-39. 
  9. Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish). 
  10. Kaczorek, T. (2011). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin. Zbl1221.93002
  11. Kaczorek, T. (2013). Approximation of positive stable continuous-time linear systems by positive stable discrete-time systems, Pomiary Automatyka Robotyka 59 (2): 359-364. Zbl1279.93062
  12. Kaczorek, T. (2011). Necessary and sufficient conditions of stability of fractional positive continuous-time linear systems, Acta Mechanica et Automatica 5(2): 52-54. 

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