Details

Title

Practical and asymptotic stability of fractional discrete-time scalar systems described by a new model

Journal title

Archives of Control Sciences

Yearbook

2016

Numer

No 4

Publication authors

Divisions of PAS

Nauki Techniczne

Abstract

<jats:title>Abstract</jats:title> <jats:p> The stability problems of fractional discrete-time linear scalar systems described by the new model are considered. Using the classical D-partition method, the necessary and sufficient conditions for practical stability and asymptotic stability are given. The considerations are il-lustrated by numerical examples.</jats:p>

Publisher

Committee of Automatic Control and Robotics PAS

Date

2016

Identifier

ISSN 1230-2384

References

OSTALCZYK (2012), Equivalent descriptions of a discrete - time fractional - order linear system and its stability domains and, Applied Mathematics Computer Science, 22, 533. ; RUSZEWSKI (2013), Stability conditions of fractional discrete - time scalar systems with two delays In Advances in the Theory and Applications of Non - integer Order Systems ( Lecture Notes in Electrical eds Springer - Verlag, Engineering, 257. ; STANISŁAWSKI (2013), Stability analysis for discrete - time fractional - order LTI state - space systems Part I New necessary and sufficient conditions for asymptotic stability Bulletin of the Polish Academy of, Sciences, 61, 353. ; BUSŁOWICZ (2012), Stability analysis of continuous - time linear systems consisting of n subsystems with different fractional orders Bulletin of the Polish of, Academy Sciences Technical Sciences, 60, 279. ; BUSŁOWICZ (2009), Simple conditions for practical stability of linear positive fractional discrete - time linear systems of Applied Mathematics and, Computer Science, 19, 263. ; BUSŁOWICZ (2012), Simple analytic conditions for stability of fractional discretetime linear systems with diagonal state matrix Bulletin of the Polish of, Academy Sciences Technical Sciences, 60, 809. ; OPRZĘDKIEWICZ (2016), A non integer order , state space model for one dimensional heat transfer process Archives of Control, Sciences, 26, 261. ; BUSŁOWICZ (2016), Stability conditions for linear continuous - time fractional - order state - delayed systems Bulletin of the Polish of, Academy Sciences Technical Sciences, 64, 3. ; GRYAZINA (2008), decomposition technique state - of - the - art Automation and, Remote Control, 69, 1991, doi.org/10.1134/S0005117908120011 ; KACZOREK (2016), Responses comparison of the two discretetime linear fractional state - space models Fractional Calculus and Applied, Analysis, 19, 789. ; BUSŁOWICZ (2013), Necessary and sufficient conditions for stability of fractional discrete - time linear state - space systems Bulletin of the Polish of, Academy Sciences Technical Sciences, 61, 779. ; KACZOREK (2008), Practical stability of positive fractional discrete - time systems Bulletin of the Polish of, Academy Sciences Technical Sciences, 56, 313. ; BUSŁOWICZ (2011), Stability of state - space models of linear continuous - time fractional order systems et, Acta Mechanica Automatica, 5, 15.

DOI

10.1515/acsc-2016-0024

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