On the Stability of Linear Incommensurate Fractional-Order Difference Systems
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 judg...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-10-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/10/1754 |
| _version_ | 1797551246575403008 |
|---|---|
| author | Noureddine Djenina Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham |
| author_facet | Noureddine Djenina Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham |
| author_sort | Noureddine Djenina |
| collection | DOAJ |
| description | 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 <i>Z</i>-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems. |
| first_indexed | 2024-03-10T15:41:51Z |
| format | Article |
| id | doaj.art-dc1ebbdb65984916a460fdc9b271f753 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:41:51Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-dc1ebbdb65984916a460fdc9b271f7532023-11-20T16:48:26ZengMDPI AGMathematics2227-73902020-10-01810175410.3390/math8101754On the Stability of Linear Incommensurate Fractional-Order Difference SystemsNoureddine Djenina0Adel Ouannas1Iqbal M. Batiha2Giuseppe Grassi3Viet-Thanh Pham4Laboratory of Mathematics, Informatics and Systems (LAMIS), University of Laarbi Tebessi, Tebessa 12002, AlgeriaLaboratory of Mathematics, Informatics and Systems (LAMIS), University of Laarbi Tebessi, Tebessa 12002, AlgeriaDepartment of Mathematics, University of Jordan, Amman 11942, JordanDipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, ItalyNonlinear Systems and Applications, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 758307, VietnamTo 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 <i>Z</i>-transform method. All results of this work are verified numerically by illustrating some examples that deal with the stability of solutions of such systems.https://www.mdpi.com/2227-7390/8/10/1754<i>Z</i>-transform methodlinear incommensurate fractional-order difference systemstability |
| spellingShingle | Noureddine Djenina Adel Ouannas Iqbal M. Batiha Giuseppe Grassi Viet-Thanh Pham On the Stability of Linear Incommensurate Fractional-Order Difference Systems Mathematics <i>Z</i>-transform method linear incommensurate fractional-order difference system stability |
| title | On the Stability of Linear Incommensurate Fractional-Order Difference Systems |
| title_full | On the Stability of Linear Incommensurate Fractional-Order Difference Systems |
| title_fullStr | On the Stability of Linear Incommensurate Fractional-Order Difference Systems |
| title_full_unstemmed | On the Stability of Linear Incommensurate Fractional-Order Difference Systems |
| title_short | On the Stability of Linear Incommensurate Fractional-Order Difference Systems |
| title_sort | on the stability of linear incommensurate fractional order difference systems |
| topic | <i>Z</i>-transform method linear incommensurate fractional-order difference system stability |
| url | https://www.mdpi.com/2227-7390/8/10/1754 |
| work_keys_str_mv | AT noureddinedjenina onthestabilityoflinearincommensuratefractionalorderdifferencesystems AT adelouannas onthestabilityoflinearincommensuratefractionalorderdifferencesystems AT iqbalmbatiha onthestabilityoflinearincommensuratefractionalorderdifferencesystems AT giuseppegrassi onthestabilityoflinearincommensuratefractionalorderdifferencesystems AT vietthanhpham onthestabilityoflinearincommensuratefractionalorderdifferencesystems |