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A generalisation of Fuhrmann’s rank condition for discrete dynamic systems

A generalisation of Fuhrmann’s rank condition for discrete dynamic systems 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of System of Systems Engineering Inderscience Publishers

A generalisation of Fuhrmann’s rank condition for discrete dynamic systems

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Publisher
Inderscience Publishers
Copyright
Copyright © Inderscience Enterprises Ltd. All rights reserved
ISSN
1748-0671
eISSN
1748-068X
DOI
10.1504/IJSSE.2011.043864
Publisher site
See Article on Publisher Site

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.

Journal

International Journal of System of Systems EngineeringInderscience Publishers

Published: Jan 1, 2011

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