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

Research output: Contribution to conference typesPaper

Jing Li, Mark French

Original languageEnglish
Publication statusPublished - 2013

Bibliographical note

Control Conference (ECC), 2013 European ; Conference date: 17-07-2013 Through 19-07-2013

King's Authors


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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