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On invariant zeros of linear systems of PDEs

On invariant zeros of linear systems of PDEs
On invariant zeros of linear systems of PDEs
In this paper we provide a behavioral framework in which to describe and extend the concept of linear dynamics introduced by Fliess, from the one dimensional (1D) to the multidimensional (nD) framework.We provide an alternative description of the invariant zeros of a system, equivalent to the Smith zero description in the 1D case and use this to generalize the concept and characterization of invariant zeros to the nD case. In particular we show that the definitions are equivalent in the 1D case to those in the classical literature. We provide new results on the structural relations of nD invariant and transmission zeros.
multidimensional linearsystem, behavioral approach, invariantzeros, oberst duality, characteristic variety
0024-3795
275-297
Zaris, P.
99d0caa1-82f0-4b36-8c41-84b68ae8ca96
Wood, J.
65587872-7126-469a-851a-d60195d39058
Pillai, H.
be18e6fa-cab8-431f-80db-4926e48074c5
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Zaris, P.
99d0caa1-82f0-4b36-8c41-84b68ae8ca96
Wood, J.
65587872-7126-469a-851a-d60195d39058
Pillai, H.
be18e6fa-cab8-431f-80db-4926e48074c5
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72

Zaris, P., Wood, J., Pillai, H. and Rogers, E. (2006) On invariant zeros of linear systems of PDEs. Linear Algebra and Its Applications, 417 (1), 275-297. (doi:10.1016/j.laa.2005.10.025).

Record type: Article

Abstract

In this paper we provide a behavioral framework in which to describe and extend the concept of linear dynamics introduced by Fliess, from the one dimensional (1D) to the multidimensional (nD) framework.We provide an alternative description of the invariant zeros of a system, equivalent to the Smith zero description in the 1D case and use this to generalize the concept and characterization of invariant zeros to the nD case. In particular we show that the definitions are equivalent in the 1D case to those in the classical literature. We provide new results on the structural relations of nD invariant and transmission zeros.

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e-pub ahead of print date: 22 December 2005
Published date: 1 August 2006
Keywords: multidimensional linearsystem, behavioral approach, invariantzeros, oberst duality, characteristic variety
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 264342
URI: http://eprints.soton.ac.uk/id/eprint/264342
ISSN: 0024-3795
PURE UUID: 35d4f2e7-e522-4196-bc2b-53af7e1709e4
ORCID for E. Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 24 Jul 2007
Last modified: 20 Jul 2019 01:23

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