Connections between Georgiou and Smith's robust stability type theorems and the nonlinear small-gain theorems
Connections between Georgiou and Smith's robust stability type theorems and the nonlinear small-gain theorems
Georgiou and Smith's robust stability theorem using the concept of nonlinear gap metric is shown to be equivalent to the traditional nonlinear small-gain theorem for feedback systems with parts of zero input disturbances. We present both global and local forms of the nonlinear small-gain theorem establishing existence and boundedness properties simultaneously in this paper; and the results are used to show the corresponding types of Georgiou and Smith's robust stability theorem.
nonlinear small-gain theorem, robust stability theorem, nonlinear gap metric, schauder's fixed point theorem
1-16
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
(2014)
Connections between Georgiou and Smith's robust stability type theorems and the nonlinear small-gain theorems.
SIAM Journal on Control and Optimization, .
(Submitted)
Abstract
Georgiou and Smith's robust stability theorem using the concept of nonlinear gap metric is shown to be equivalent to the traditional nonlinear small-gain theorem for feedback systems with parts of zero input disturbances. We present both global and local forms of the nonlinear small-gain theorem establishing existence and boundedness properties simultaneously in this paper; and the results are used to show the corresponding types of Georgiou and Smith's robust stability theorem.
This record has no associated files available for download.
More information
Submitted date: 2014
Keywords:
nonlinear small-gain theorem, robust stability theorem, nonlinear gap metric, schauder's fixed point theorem
Organisations:
Southampton Wireless Group
Identifiers
Local EPrints ID: 363497
URI: http://eprints.soton.ac.uk/id/eprint/363497
PURE UUID: 67c9565a-a709-4081-b2e4-e6711f5127b0
Catalogue record
Date deposited: 25 Mar 2014 14:46
Last modified: 11 Dec 2021 03:55
Export record
Contributors
Author:
Jing Li
Author:
Mark French
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics