An analysis of the stability boundary for a linear fractional difference system

Tomáš Kisela

Mathematica Bohemica (2015)

  • Volume: 140, Issue: 2, page 195-203
  • ISSN: 0862-7959

Abstract

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This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.

How to cite

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Kisela, Tomáš. "An analysis of the stability boundary for a linear fractional difference system." Mathematica Bohemica 140.2 (2015): 195-203. <http://eudml.org/doc/271579>.

@article{Kisela2015,
abstract = {This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.},
author = {Kisela, Tomáš},
journal = {Mathematica Bohemica},
keywords = {fractional difference system; stability; Laplace transform},
language = {eng},
number = {2},
pages = {195-203},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {An analysis of the stability boundary for a linear fractional difference system},
url = {http://eudml.org/doc/271579},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Kisela, Tomáš
TI - An analysis of the stability boundary for a linear fractional difference system
JO - Mathematica Bohemica
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 140
IS - 2
SP - 195
EP - 203
AB - This paper deals with basic stability properties of a two-term linear autonomous fractional difference system involving the Riemann-Liouville difference. In particular, we focus on the case when eigenvalues of the system matrix lie on a boundary curve separating asymptotic stability and unstability regions. This issue was posed as an open problem in the paper J. Čermák, T. Kisela, and L. Nechvátal (2013). Thus, the paper completes the stability analysis of the corresponding fractional difference system.
LA - eng
KW - fractional difference system; stability; Laplace transform
UR - http://eudml.org/doc/271579
ER -

References

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  3. Čermák, J., Kisela, T., Nechvátal, L., 10.1016/j.amc.2012.12.019, Appl. Math. Comput. 219 (2013), 7012-7022. (2013) Zbl1288.34005MR3027865DOI10.1016/j.amc.2012.12.019
  4. Čermák, J., Kisela, T., Nechvátal, L., Stability and asymptotic properties of a linear fractional difference equation, Adv. Difference Equ. (electronic only) (2012),2012:122 14 pages. (2012) MR2972648
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  12. Petráš, I., Stability of fractional-order systems with rational orders: A survey, Fract. Calc. Appl. Anal. 12 (2009), 269-298. (2009) Zbl1182.26017MR2572711
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  14. Qian, D., Li, C., Agarwal, R. P., Wong, P. J. Y., 10.1016/j.mcm.2010.05.016, Math. Comput. Modelling 52 (2010), 862-874. (2010) Zbl1202.34020MR2661771DOI10.1016/j.mcm.2010.05.016

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