Title: A generalisation of Fuhrmann's rank condition for discrete dynamic systems

Authors: Sándor Molnár; Ferenc Szigeti

Addresses: Department of Informatics, Szent Istvan University, H-2103 Gödöllö, Páter K. u.1., Hungary. ' Department of Control Engineering, University of los Andes, Merida, Venezuela

Abstract: For discrete-time linear systems, controllability and reachability are not equivalent. Instead of the well-known Kalman|s rank condition, which characterises reachability, controllability to origin of the time invariant, discrete-time linear system is equivalent to the Fuhrmann|s rank condition. In the first part of this paper, we prove that controllability to origin of time varying discrete-time linear systems, under a difference-algebraic condition, is equivalent to a generalised Fuhrmann|s rank condition. In the second part, we prove that reachability and observability for time varying discrete-time linear systems are equivalent to a structured Kalman|s rank condition, under the difference algebraic independence of the structure matrices.

Keywords: discrete time linear systems; difference algebraic conditions; rank condition; reachability; controllability.

DOI: 10.1504/IJSSE.2011.043864

International Journal of System of Systems Engineering, 2011 Vol.2 No.4, pp.279 - 289

Published online: 16 Oct 2014 *

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