Stability of nonlinear h -difference systems with n fractional orders

Małgorzata Wyrwas; Ewa Pawluszewicz; Ewa Girejko

Kybernetika (2015)

  • Volume: 51, Issue: 1, page 112-136
  • ISSN: 0023-5954

Abstract

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In the paper we study the subject of stability of systems with h -differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with n fractional orders. The equivalent descriptions of fractional h -difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with n -orders.

How to cite

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Wyrwas, Małgorzata, Pawluszewicz, Ewa, and Girejko, Ewa. "Stability of nonlinear $h$-difference systems with $n$ fractional orders." Kybernetika 51.1 (2015): 112-136. <http://eudml.org/doc/270056>.

@article{Wyrwas2015,
abstract = {In the paper we study the subject of stability of systems with $h$-differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with $n$ fractional orders. The equivalent descriptions of fractional $h$-difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with $n$-orders.},
author = {Wyrwas, Małgorzata, Pawluszewicz, Ewa, Girejko, Ewa},
journal = {Kybernetika},
keywords = {fractional difference systems; difference operators; stability; fractional difference systems; difference operators; asymptotic stability; Lyapunov direct method},
language = {eng},
number = {1},
pages = {112-136},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Stability of nonlinear $h$-difference systems with $n$ fractional orders},
url = {http://eudml.org/doc/270056},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Wyrwas, Małgorzata
AU - Pawluszewicz, Ewa
AU - Girejko, Ewa
TI - Stability of nonlinear $h$-difference systems with $n$ fractional orders
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 1
SP - 112
EP - 136
AB - In the paper we study the subject of stability of systems with $h$-differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with $n$ fractional orders. The equivalent descriptions of fractional $h$-difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with $n$-orders.
LA - eng
KW - fractional difference systems; difference operators; stability; fractional difference systems; difference operators; asymptotic stability; Lyapunov direct method
UR - http://eudml.org/doc/270056
ER -

References

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