On the state of behaviors
On the state of behaviors
The theme of the present paper is the study of the concept of state and the corresponding state maps in the context of Willems’ behavioral theory. We concentrate on Markovian system and their representation in terms of first order difference or differential systems. We follow by a full analysis of the special case of state systems, the embedding of a linear system in a state system via the use of state maps arriving at state representations or, equivalently, to a realization theory for behaviors. Minimality is defined and characterized and a state space isomorphism theorem is established. Realization procedures based on the shift realization are developed as well as a rigorous analysis of the construction of state maps. The paper owes much to Rapisarda and Willems [1997].
behaviors, behavior homomorphisms, Markovian systems, state systems, realization theory, state maps, state space isomorphisms.
570-614
Fuhrmann, Paul A.
650a7155-960a-478c-8348-7761c7f4b6e1
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Yamamoto, Yutaka
5625267f-f8a4-4ec5-8c95-72988e47fc1f
September 2007
Fuhrmann, Paul A.
650a7155-960a-478c-8348-7761c7f4b6e1
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Yamamoto, Yutaka
5625267f-f8a4-4ec5-8c95-72988e47fc1f
Fuhrmann, Paul A., Rapisarda, Paolo and Yamamoto, Yutaka
(2007)
On the state of behaviors.
Linear Algebra and Its Applications, 424 (2-3), .
Abstract
The theme of the present paper is the study of the concept of state and the corresponding state maps in the context of Willems’ behavioral theory. We concentrate on Markovian system and their representation in terms of first order difference or differential systems. We follow by a full analysis of the special case of state systems, the embedding of a linear system in a state system via the use of state maps arriving at state representations or, equivalently, to a realization theory for behaviors. Minimality is defined and characterized and a state space isomorphism theorem is established. Realization procedures based on the shift realization are developed as well as a rigorous analysis of the construction of state maps. The paper owes much to Rapisarda and Willems [1997].
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Published date: September 2007
Keywords:
behaviors, behavior homomorphisms, Markovian systems, state systems, realization theory, state maps, state space isomorphisms.
Organisations:
Southampton Wireless Group
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Local EPrints ID: 262203
URI: http://eprints.soton.ac.uk/id/eprint/262203
PURE UUID: 4ef64754-5dab-4fe7-a3b7-af984d0d6181
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Date deposited: 29 Mar 2006
Last modified: 14 Mar 2024 07:07
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Contributors
Author:
Paul A. Fuhrmann
Author:
Paolo Rapisarda
Author:
Yutaka Yamamoto
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