On the state of behaviors

P. A. Fuhrmann; P. Rapisarda; Y. Yamamoto

doi:10.1016/j.laa.2007.02.028

On the state of behaviors

P. A. Fuhrmann, P. Rapisarda, Y. Yamamoto

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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 [P. Rapisarda, J.C. Willems, State maps for linear systems, SIAM J. Contr. Optim. 35 (1997) 1053-1091].

Original language	English
Pages (from-to)	570-614
Number of pages	45
Journal	Linear Algebra and Its Applications
Volume	424
Issue number	2-3
DOIs	https://doi.org/10.1016/j.laa.2007.02.028
State	Published - 15 Jul 2007

Keywords

Behavior homomorphisms
Behaviors
Markovian systems
Realization theory
State maps
State space isomorphisms
State systems

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2007.02.028

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title = "On the state of behaviors",

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 [P. Rapisarda, J.C. Willems, State maps for linear systems, SIAM J. Contr. Optim. 35 (1997) 1053-1091].",

keywords = "Behavior homomorphisms, Behaviors, Markovian systems, Realization theory, State maps, State space isomorphisms, State systems",

author = "Fuhrmann, {P. A.} and P. Rapisarda and Y. Yamamoto",

note = "Funding Information: ∗ Corresponding author. E-mail address: [email protected] (P.A. Fuhrmann). 1 Partially supported by ISF under Grant No. 1282/05.",

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AU - Rapisarda, P.

AU - Yamamoto, Y.

N1 - Funding Information: ∗ Corresponding author. E-mail address: [email protected] (P.A. Fuhrmann). 1 Partially supported by ISF under Grant No. 1282/05.

PY - 2007/7/15

Y1 - 2007/7/15

N2 - 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 [P. Rapisarda, J.C. Willems, State maps for linear systems, SIAM J. Contr. Optim. 35 (1997) 1053-1091].

AB - 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 [P. Rapisarda, J.C. Willems, State maps for linear systems, SIAM J. Contr. Optim. 35 (1997) 1053-1091].

KW - Behavior homomorphisms

KW - Behaviors

KW - Markovian systems

KW - Realization theory

KW - State maps

KW - State space isomorphisms

KW - State systems

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JF - Linear Algebra and Its Applications

IS - 2-3

ER -

On the state of behaviors

Abstract

Keywords

ASJC Scopus subject areas

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