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

International Journal of Applied Mathematics and Computer Science (2013)

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

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topTadeusz 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

top- Berman, A. and Plemmons, R.J. (1994). Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA. Zbl0815.15016
- Busłowicz, M. (2008). Stability of linear continuous-time fractional order systems with delays of the retarded type, Bulletin of the Polish Academy of Sciences: Technical Sciences 56(4): 319-324.
- Busłowicz, M. (2012). Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders, Bulletin of the Polish Academy of Sciences: Technical Sciences 60(2): 279-284.
- 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
- Farina, L. and Rinaldi, S. (2000). Positive Linear Systems: Theory and Applications, J. Wiley, New York, NY. Zbl0988.93002
- Gantmakher, F.R. (1959). Theory of Matrices, Chelsea Pub. Co., New York, NY. Zbl0050.24804
- Kaczorek, T. (2002). Positive 1D and 2D Systems, Springer-Verlag, London. Zbl1005.68175
- 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.
- Kaczorek, T. (1998). Vectors and Matrices in Automation and Electrotechnics, WNT, Warsaw, (in Polish).
- Kaczorek, T. (2011). Selected Problems of Fractional System Theory, Springer-Verlag, Berlin. Zbl1221.93002
- 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
- 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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