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Robust stability of input-output systems with initial conditions Robust Stability of Input-Output Systems with Initial Conditions

Liu, Jing and French, Mark (2015) Robust stability of input-output systems with initial conditions Robust Stability of Input-Output Systems with Initial Conditions SIAM Journal on Control and Optimization, 53, (3), pp. 1625-1653. (doi:10.1137/120903373).

Record type: Article

Abstract

We consider the development of a general nonlinear input-output theory which encompasses systems with initial conditions. Systems are defined in a set theoretic manner from input-output pairs on a doubly infinite time axis, and a general construction of the initial conditions is given in terms of an equivalence class of trajectories on the negative time axis. Input-output operators are then defined for given initial conditions, and a suitable notion of input-output stability on the positive time axis with initial conditions is given. This notion of stability is closely related to the ISS/IOS concepts of Sontag. A fundamental robust stability theorem is derived which represents a generalization of the input-output operator robust stability theorem of Georgiou and Smith, to include the case of initial conditions. This includes a suitable generalization of the nonlinear gap metric. Some applications are given to show the utility of the robust stability theorem.

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More information

Accepted/In Press date: 20 January 2015
Published date: 25 June 2015
Keywords: nonlinear systems, robust stability, gap metric, feedback connection, small-gain-like stability theorem, ISS/IOS
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 388531
URI: http://eprints.soton.ac.uk/id/eprint/388531
PURE UUID: 0231bc67-3fec-4d45-910c-c81484f6e302

Catalogue record

Date deposited: 29 Feb 2016 10:26
Last modified: 17 Jul 2017 19:37

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Contributors

Author: Jing Liu
Author: Mark French

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