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Discrete Dynamics in Nature and Society
Volume 2014 (2014), Article ID 183782, 8 pages
http://dx.doi.org/10.1155/2014/183782
Research Article

Multiparameter Fractional Difference Linear Control Systems

Faculty of Computer Science, Bialystok University of Technology, Wiejska 45A, 15-351 Bialystok, Poland

Received 3 November 2013; Revised 2 January 2014; Accepted 7 January 2014; Published 2 March 2014

Academic Editor: Garyfalos Papashinopoulos

Copyright © 2014 Dorota Mozyrska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.