The University of Southampton
University of Southampton Institutional Repository

General Fast Sampling Theorems for Nonlinear Systems

General Fast Sampling Theorems for Nonlinear Systems
General Fast Sampling Theorems for Nonlinear Systems
This paper is concerned with the gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances in both input and output channels. The principal idea is to construct a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap between the two controllers. It is expected that, under general conditions, the computed gap depends on the discrete sample size and the faster the sample rate, the smaller the gap and, therefore, existing gap metric robust stability theorems can be applied to obtain both stability and performance results for the appropriately discretised controller. This is shown for the case of memoryless controllers and for a more general class of controllers specified by stable, causal operators. In both cases, both regional and global results are obtained under respective local and global incremental stability assumptions on the controllers.
1037-1050
Bian, W
3f636243-2f84-4d56-8c78-b29fbe6571c7
French, M
22958f0e-d779-4999-adf6-2711e2d910f8
Bian, W
3f636243-2f84-4d56-8c78-b29fbe6571c7
French, M
22958f0e-d779-4999-adf6-2711e2d910f8

Bian, W and French, M (2005) General Fast Sampling Theorems for Nonlinear Systems. Systems & Control Letters, 54, 1037-1050.

Record type: Article

Abstract

This paper is concerned with the gap metric approach to controller discretisation problems for continuous-time nonlinear systems with disturbances in both input and output channels. The principal idea is to construct a discrete controller based on a given stabilizing continuous time controller via a fast sampling and hold procedure and to calculate the gap between the two controllers. It is expected that, under general conditions, the computed gap depends on the discrete sample size and the faster the sample rate, the smaller the gap and, therefore, existing gap metric robust stability theorems can be applied to obtain both stability and performance results for the appropriately discretised controller. This is shown for the case of memoryless controllers and for a more general class of controllers specified by stable, causal operators. In both cases, both regional and global results are obtained under respective local and global incremental stability assumptions on the controllers.

Text
DigitalControllerFinal.pdf - Other
Download (228kB)

More information

Published date: October 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 261490
URI: http://eprints.soton.ac.uk/id/eprint/261490
PURE UUID: 8bfec586-034e-4e1f-ace6-f0e7bb3ee68f

Catalogue record

Date deposited: 20 Oct 2005
Last modified: 14 Mar 2024 06:53

Export record

Contributors

Author: W Bian
Author: M 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

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×