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Abstract

In this paper the controllability properties of the convex linear combination of fractional, linear, discrete-time systems are characterized and investigated. The notions of linear convex combination and controllability in the context of fractional-order systems are recalled. Then, the controllability property of such a linear combination of discrete-time, linear fractional systems is proven. Further, the reduction of an infinite problem of transition matrix derivation is reduced to a finite one, which greatly simplifies the numerical burden of the controllability issue. Examples of controllable and uncontrollable, single-input, linear systems are presented. The possibility of extension of the considerations to multi-input systems is shown.
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Authors and Affiliations

Tadeusz Kaczorek
1
ORCID: ORCID
Jerzy Klamka
2
ORCID: ORCID
Andrzej Dzieliński
3
ORCID: ORCID

  1. Bialystok University of Technology, Faculty of Electrical Engineering, ul. Wiejska 45D, Bialystok, Poland
  2. Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, Gliwice, Poland
  3. Warsaw University of Technology, Faculty of Electrical Engineering, ul. Koszykowa 75, Warsaw, Poland

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