Analysis of the fractional descriptor discrete-time linear systems by the use of the shuffle algorithm

Tadeusz Kaczorek; Andrzej Ruszewski

doi:10.3934/jcd.2021007

Article Contents

2021, Volume 8, Issue 2: 153-163. Doi: 10.3934/jcd.2021007

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Analysis of the fractional descriptor discrete-time linear systems by the use of the shuffle algorithm

Tadeusz Kaczorek and
Andrzej Ruszewski^,

Faculty of Electrical Engineering, Bialystok University of Technology, Wiejska 45D, 15-351 Biaƚystok, Poland

^* Corresponding author: Andrzej Ruszewski
^* Corresponding author: Andrzej Ruszewski

Received: September 30, 2020

Revised: November 30, 2020

Early access: March 2021

Published: April 2021

This work was supported by National Science Centre in Poland under Grant No. 2017/27/B/ST7/02443

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Abstract

The shuffle algorithm is applied to analysis of the fractional descriptor discrete-time linear systems. Using the shuffle algorithm the singularity of the fractional descriptor linear system is eliminated and the system is decomposed into dynamic and static parts. Procedures for computation of the solution and dynamic and static parts of the system are proposed. Sufficient conditions for the positivity of the fractional descriptor discrete-time linear systems are established.

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Mathematics Subject Classification: Primary: 93C05; Secondary: 93C55, 26A33.

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