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A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions

A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions
A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions
We consider the development of a general nonlinear small-gain theorem for systems with abstract 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 (i.e. a state at time zero) is given in terms of an equivalence class of trajectories on the negative time axis. By using this formulation, an ISS-type nonlinear small-gain theorem is established with complete disconnection between the stability property and the existence, uniqueness properties. We provide an illustrative example.
nonlinear system theory, stability of nonlinear systems, behavioural systems
1699-1704
Li, Jing
fafa4088-5b81-4c81-9228-ae4da619d9ff
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Li, Jing
fafa4088-5b81-4c81-9228-ae4da619d9ff
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8

Li, Jing and French, Mark (2013) A generalisation of the nonlinear small-gain theorem for systems with abstract initial conditions. Control Conference (ECC), 2013 European, Zurich, Switzerland. 17 - 19 Jul 2013. pp. 1699-1704 .

Record type: Conference or Workshop Item (Paper)

Abstract

We consider the development of a general nonlinear small-gain theorem for systems with abstract 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 (i.e. a state at time zero) is given in terms of an equivalence class of trajectories on the negative time axis. By using this formulation, an ISS-type nonlinear small-gain theorem is established with complete disconnection between the stability property and the existence, uniqueness properties. We provide an illustrative example.

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Published date: 2013
Venue - Dates: Control Conference (ECC), 2013 European, Zurich, Switzerland, 2013-07-17 - 2013-07-19
Keywords: nonlinear system theory, stability of nonlinear systems, behavioural systems
Organisations: Southampton Wireless Group

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Local EPrints ID: 355085
URI: http://eprints.soton.ac.uk/id/eprint/355085
PURE UUID: 363cc596-f9ae-41c5-be44-161af50e5c7a

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Date deposited: 19 Aug 2013 15:20
Last modified: 14 Mar 2024 14:28

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Contributors

Author: Jing Li
Author: Mark French

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