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Causal and Stable Input/Output Structures on Multidimensional Behaviours

Wood, J, Sule, V R and Rogers, E (2005) Causal and Stable Input/Output Structures on Multidimensional Behaviours SIAM Journal on Control and Optimization, 43, (4), pp. 1493-1520.

Record type: Article

Abstract

In this work we study multidimensional (nD) linear differential behaviours with a distinguished independent variable called "time". We define in a natural way causality and stability on input/output structures with respect to this distinguished direction. We make an extension of some results in the theory of partial differential equations, demonstrating that causality is equivalent to a property of the transfer matrix which is essentially hyperbolicity of the Pc operator defining the behaviour (Bc)0,y We also quote results which in effect characterise time autonomy for the general systems case. Stability is likewise characterized by a property of the transfer matrix. We prove this result for the 2D case and for the case of a single equation; for the general case it requires solution of an open problem concerning the geometry of a particular set in Cn. In order to characterize input/output stability we also develop new results on inclusions of kernels, freeness of variables, and closure with respect to S,S' and associated spaces, which are of independent interest. We also discuss stability of autonomous behaviours, which we beleive to be governed by a corresponding condition.

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Published date: 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 259276
URI: http://eprints.soton.ac.uk/id/eprint/259276
PURE UUID: 85b0bdb2-b1d1-46d1-acc5-18945f8c7c0f

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Date deposited: 08 Mar 2005
Last modified: 18 Jul 2017 09:24

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Contributors

Author: J Wood
Author: V R Sule
Author: E Rogers

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