# Controllability of Positive Discrete-Time Switched Fractional Order Systems for Fixed Switching Sequence

• Artur Babiarz
• Michał Niezabitowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9875)

## Abstract

In the article unconstrained controllability problem of positive discrete-time switched fractional order systems is addressed. A solution of discrete-time switched fractional order systems is presented. Additionally, a transition matrix of considered dynamical systems is given. A sufficient condition for unconstrained controllability in a given number of steps is formulated and proved using the general formula of solution of difference state equation. Finally, the illustrative examples are also presented.

## Keywords

Controllability Switched system Fractional order system

## Notes

### Acknowledgment

The research presented here was done by first and third author as part of the project funded by the National Science Centre in Poland granted according to decision DEC-2014/13/B/ST7/00755. Moreover, the work of the second author was supported by Polish Ministry for Science and Higher Education under internal grant BKM/506/RAU1/2016 t.1 for Institute of Automatic Control, Silesian University of Technology, Gliwice, Poland. Finally, the calculations were performed with the use of IT infrastructure of GeCONiI Upper Silesian Centre for Computational Science and Engineering (NCBiR grant no POIG.02.03.01-24-099/13).

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© Springer International Publishing Switzerland 2016

## Authors and Affiliations

• Artur Babiarz
• 1
Email author