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Controllable and autonomous nD linear systems

Controllable and autonomous nD linear systems
Controllable and autonomous nD linear systems
The theory of multidimensional systems suffers in certain areas from a lack of development of fundamental concepts. Using the behavioural approach, the study of linear shift-invariant nD systems can be encompassed within the well-established framework of commutative algebra, as previously shown by Oberst. We consider here the discrete case. In this paper, we take two basic properties of discrete nD systems, controllability and autonomy, and show that they have simple algebraic characterizations. We make several non-trivial generalizations of previous results for the 2D case. In particular we analyse the controllable-autonomous decomposition and the controllable subsystem of autoregressive systems. We also show that a controllable nD subsystem of (k q) (Z n) is precisely one which is minimal in its transfer class.
33-69
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
3452e9bb-d3bd-4995-b4bb-424bbd288b09
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
3452e9bb-d3bd-4995-b4bb-424bbd288b09

Wood, J., Rogers, E. and Owens, D.H. (1999) Controllable and autonomous nD linear systems. Multidimensional Systems and Signal Processing, 10 (1), 33-69.

Record type: Article

Abstract

The theory of multidimensional systems suffers in certain areas from a lack of development of fundamental concepts. Using the behavioural approach, the study of linear shift-invariant nD systems can be encompassed within the well-established framework of commutative algebra, as previously shown by Oberst. We consider here the discrete case. In this paper, we take two basic properties of discrete nD systems, controllability and autonomy, and show that they have simple algebraic characterizations. We make several non-trivial generalizations of previous results for the 2D case. In particular we analyse the controllable-autonomous decomposition and the controllable subsystem of autoregressive systems. We also show that a controllable nD subsystem of (k q) (Z n) is precisely one which is minimal in its transfer class.

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Published date: January 1999
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 250453
URI: http://eprints.soton.ac.uk/id/eprint/250453
PURE UUID: 51dd37eb-a7f8-4471-94cd-cadab5fb69ee
ORCID for E. Rogers: ORCID iD orcid.org/0000-0003-0179-9398

Catalogue record

Date deposited: 29 Mar 2000
Last modified: 10 Dec 2019 01:57

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