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

Description

Archives of Control Sciences welcomes for consideration papers on topics of significance in broadly understood control science and related areas, including: basic control theory, optimal control, optimization methods, control of complex systems, mathematical modeling of dynamic and control systems, expert and decision support systems and diverse methods of knowledge modelling and representing uncertainty (by stochastic, set-valued, fuzzy or rough set methods, etc.), robotics and flexible manufacturing systems. Related areas that are covered include information technology, parallel and distributed computations, neural networks and mathematical biomedicine, mathematical economics, applied game theory, financial engineering, business informatics and other similar fields.

Aims and Scope: Archives of Control Sciences publishes papers in the broadly understood field of control science and related areas while promoting the closer integration of the Polish, as well as other Central and East European scientific communities with the international world of science.

Abstract

Abstract 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.

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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