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Robust stability of input-output systems with initial conditions

Robust stability of input-output systems with initial conditions
Robust stability of input-output systems with initial conditions
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.
nonlinear systems, robust stability, gap metric, feedback connection, small-gain-like stability theorem, ISS/IOS
1625-1653
Liu, Jing
a3428c79-3f08-43ab-9f64-ec895d5e6cba
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Liu, Jing
a3428c79-3f08-43ab-9f64-ec895d5e6cba
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8

Liu, Jing and French, Mark (2015) Robust stability of input-output systems with initial conditions. SIAM Journal on Control and Optimization, 53 (3), 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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Accepted/In Press date: 20 January 2015
e-pub ahead of print date: 25 June 2015
Published date: 25 June 2015
Keywords: nonlinear systems, robust stability, gap metric, feedback connection, small-gain-like stability theorem, ISS/IOS
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 356961
URI: https://eprints.soton.ac.uk/id/eprint/356961
PURE UUID: c36ec8aa-323e-428d-a286-aea18b70d26a

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Date deposited: 03 Oct 2013 12:46
Last modified: 16 Nov 2017 17:34

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Contributors

Author: Jing Liu
Author: Mark French

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