Reachability, observability and strict equivalence of networks of linear systems

Paul A. Fuhrmann; Uwe Helmke

doi:10.1007/s00498-012-0104-0

Reachability, observability and strict equivalence of networks of linear systems

Paul A. Fuhrmann, Uwe Helmke

Department of Mathematics

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

12 Scopus citations

Abstract

This paper aims at a better understanding of reachability and observability properties of heterogeneous networks of linear systems. It extends prior work by Hara et al. (SICE J Control Meas Syst Integr 2:299-306, 2009), who characterized reachability for homogeneous networks of identical linear SISO systems. Our approach is based on extending the classical notion of strict system equivalence to networks of linear systems. We survey and extend known characterizations for reachability and observability for arbitrary interconnected linear MIMO systems. Both static and dynamic interconnection laws are considered, and various applications to classes of homogeneous and heterogeneous networks are derived.

Original language	English
Pages (from-to)	437-471
Number of pages	35
Journal	Mathematics of Control, Signals, and Systems
Volume	25
Issue number	4
DOIs	https://doi.org/10.1007/s00498-012-0104-0
State	Published - 1 Dec 2013

Keywords

Interconnections
Linear systems
Networks
Observability
Reachability
System equivalence

ASJC Scopus subject areas

Control and Systems Engineering
Signal Processing
Control and Optimization
Applied Mathematics

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10.1007/s00498-012-0104-0

Cite this

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abstract = "This paper aims at a better understanding of reachability and observability properties of heterogeneous networks of linear systems. It extends prior work by Hara et al. (SICE J Control Meas Syst Integr 2:299-306, 2009), who characterized reachability for homogeneous networks of identical linear SISO systems. Our approach is based on extending the classical notion of strict system equivalence to networks of linear systems. We survey and extend known characterizations for reachability and observability for arbitrary interconnected linear MIMO systems. Both static and dynamic interconnection laws are considered, and various applications to classes of homogeneous and heterogeneous networks are derived.",

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note = "Funding Information: Support of U. Helmke by a grant HE 1858/12-2 within the German Research Foundation DFG programme SPP 1305 is gratefully acknowledged. A preliminary version of Theorem 4.1 has been derived earlier in collaboration with Jens Jordan.",

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AU - Helmke, Uwe

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N2 - This paper aims at a better understanding of reachability and observability properties of heterogeneous networks of linear systems. It extends prior work by Hara et al. (SICE J Control Meas Syst Integr 2:299-306, 2009), who characterized reachability for homogeneous networks of identical linear SISO systems. Our approach is based on extending the classical notion of strict system equivalence to networks of linear systems. We survey and extend known characterizations for reachability and observability for arbitrary interconnected linear MIMO systems. Both static and dynamic interconnection laws are considered, and various applications to classes of homogeneous and heterogeneous networks are derived.

AB - This paper aims at a better understanding of reachability and observability properties of heterogeneous networks of linear systems. It extends prior work by Hara et al. (SICE J Control Meas Syst Integr 2:299-306, 2009), who characterized reachability for homogeneous networks of identical linear SISO systems. Our approach is based on extending the classical notion of strict system equivalence to networks of linear systems. We survey and extend known characterizations for reachability and observability for arbitrary interconnected linear MIMO systems. Both static and dynamic interconnection laws are considered, and various applications to classes of homogeneous and heterogeneous networks are derived.

KW - Interconnections

KW - Linear systems

KW - Networks

KW - Observability

KW - Reachability

KW - System equivalence

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Reachability, observability and strict equivalence of networks of linear systems

Abstract

Keywords

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