On the stability of linear incommensurate fractional-order difference systems

Noureddine Djenina; Adel Ouannas; Iqbal M. Batiha; Giuseppe Grassi; Viet Thanh Pham

doi:10.3390/math8101754

On the stability of linear incommensurate fractional-order difference systems

Noureddine Djenina
, Adel Ouannas
, Iqbal M. Batiha
, Giuseppe Grassi
, Viet Thanh Pham

University of Tebessa
University of Jordan
University of Salento
Ton Duc Thang University

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

Original language	English
Article number	1754
Pages (from-to)	1-12
Number of pages	12
Journal	Mathematics
Volume	8
Issue number	10
DOIs	https://doi.org/10.3390/math8101754
State	Published - Oct 2020
Externally published	Yes

Keywords

Linear incommensurate fractional-order difference system
Stability
Z-transform method

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10.3390/math8101754

Cite this

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title = "On the stability of linear incommensurate fractional-order difference systems",

abstract = "To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.",

keywords = "Linear incommensurate fractional-order difference system, Stability, Z-transform method",

author = "Noureddine Djenina and Adel Ouannas and Batiha, \{Iqbal M.\} and Giuseppe Grassi and Pham, \{Viet Thanh\}",

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AU - Djenina, Noureddine

AU - Ouannas, Adel

AU - Batiha, Iqbal M.

AU - Grassi, Giuseppe

AU - Pham, Viet Thanh

PY - 2020/10

Y1 - 2020/10

N2 - To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

AB - To follow up on the progress made on exploring the stability investigation of linear commensurate Fractional-order Difference Systems (FoDSs), such topic of its extended version that appears with incommensurate orders is discussed and examined in this work. Some simple applicable conditions for judging the stability of these systems are reported as novel results. These results are formulated by converting the linear incommensurate FoDS into another equivalent system consists of fractional-order difference equations of Volterra convolution-type as well as by using some properties of the Z-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.

KW - Linear incommensurate fractional-order difference system

KW - Stability

KW - Z-transform method

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JF - Mathematics

IS - 10

M1 - 1754

ER -

On the stability of linear incommensurate fractional-order difference systems

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Keywords

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