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# An intrinsic behavioural approach to the gap metric

Bian, Wenming, French, Mark and Pillai, Harish (2008) An intrinsic behavioural approach to the gap metric SIAM Journal on Control and Optimization, 47, (4), pp. 1939-1960.

Record type: Article

## Abstract

An intrinsic trajectory level approach without any recourse to an algebraic structure of a representation is utilized to develop a behavioural approach to robust stability. In particular it is shown how the controllable behaviour can be constructed at the trajectory level via Zorn's Lemma, and this is utilized to study the controllable-autonomous decomposition. Stability concepts are defined and the relation between this framework and the well known difficulties of classical input-output approaches to systems over the doubly infinite time-axis are discussed. The gap distance is generalised to the behavioural setting via a trajectory level definition; and a basic robust stability theorem is established for linear shift invariant behaviours. The robust stability theorem is shown to provide an explicit robustness interpretation to the behavioural $H^\infty$ synthesis of Willems and Trentelmann

PDF SIAM240507.pdf - Version of Record

Published date: 2008
Organisations: Southampton Wireless Group

## Identifiers

Local EPrints ID: 266895
URI: http://eprints.soton.ac.uk/id/eprint/266895
PURE UUID: e608ac70-626a-44bd-b55d-911928bf568b

## Catalogue record

Date deposited: 10 Nov 2008 12:07

## Contributors

Author: Wenming Bian
Author: Mark French
Author: Harish Pillai