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.
db24b8ef-282b-47c0-9cd2-75e91d312ad7
January 1999
Wood, J.
65587872-7126-469a-851a-d60195d39058
Rogers, E.
611b1de0-c505-472e-a03f-c5294c63bb72
Owens, D.H.
db24b8ef-282b-47c0-9cd2-75e91d312ad7
Wood, J., Rogers, E. and Owens, D.H.
(1999)
Controllable and autonomous nD linear systems.
Multidimensional Systems and Signal Processing, 10 (1), .
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
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Local EPrints ID: 250453
URI: http://eprints.soton.ac.uk/id/eprint/250453
PURE UUID: 51dd37eb-a7f8-4471-94cd-cadab5fb69ee
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Date deposited: 29 Mar 2000
Last modified: 18 Oct 2022 01:32
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Author:
J. Wood
Author:
E. Rogers
Author:
D.H. Owens
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