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Robust stabilization by linear output delay feedback

Robust stabilization by linear output delay feedback
Robust stabilization by linear output delay feedback
The main result establishes that if a controller $C$ (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant $P$, then global stabilization of $P$ can also be achieved by an output feedback controller $C[h]$ where the output derivatives in $C$ are replaced by an Euler approximation with sufficiently small delay $h>0$. This is proved within the conceptual framework of the nonlinear gap metric approach to robust stability. The main result is then applied to finite dimensional linear minimum phase systems with unknown coefficients but known relative degree and known sign of the high frequency gain. Results are also given for systems with non-zero initial conditions.
2533-2561
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Ilchmann, Achim
5d9d7d30-6053-477e-a04a-9e1ec8ffa805
Mueller, Markus
9abd38e5-470e-479e-ba71-3e0a627431be
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Ilchmann, Achim
5d9d7d30-6053-477e-a04a-9e1ec8ffa805
Mueller, Markus
9abd38e5-470e-479e-ba71-3e0a627431be

French, Mark, Ilchmann, Achim and Mueller, Markus (2009) Robust stabilization by linear output delay feedback. SIAM Journal on Control and Optimization, 48 (4), 2533-2561. (doi:10.1137/080726070).

Record type: Article

Abstract

The main result establishes that if a controller $C$ (comprising of a linear feedback of the output and its derivatives) globally stabilizes a (nonlinear) plant $P$, then global stabilization of $P$ can also be achieved by an output feedback controller $C[h]$ where the output derivatives in $C$ are replaced by an Euler approximation with sufficiently small delay $h>0$. This is proved within the conceptual framework of the nonlinear gap metric approach to robust stability. The main result is then applied to finite dimensional linear minimum phase systems with unknown coefficients but known relative degree and known sign of the high frequency gain. Results are also given for systems with non-zero initial conditions.

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Published date: 2009
Organisations: Southampton Wireless Group

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Local EPrints ID: 266884
URI: http://eprints.soton.ac.uk/id/eprint/266884
PURE UUID: 832aa64c-e6bc-430b-843c-7147ca83d329

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Date deposited: 07 Nov 2008 15:34
Last modified: 14 Mar 2024 08:37

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Contributors

Author: Mark French
Author: Achim Ilchmann
Author: Markus Mueller

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