Conditions on feedback stabilization of systems with state and input delays in banach spaces
Hadd, S.
Qing-Chang Zhong
Univ. of Liverpool, Liverpool;
This paper appears in: Decision and Control, 2007 46th IEEE Conference on
Publication Date: 12-14 Dec. 2007
On page(s): 2094-2099
Location: New Orleans, LA,
ISSN: 0191-2216
ISBN: 978-1-4244-1497-0
INSPEC Accession Number: 9885585
Digital Object Identifier: 10.1109/CDC.2007.4434487
Current Version Published: 2008-01-21
Abstract
Semigroup approach to feedback stabilization of systems with state delay has already been introduced in the literature. The aim of this work is to apply the semigroup approach to the feedback stabilization of partial differential systems with state and input delays. Here we shall work with general state Banach spaces and a general class of state and delay operators. We use a generalization of Hautus criteria to derive a necessary condition for the stabilization of the delay system. We show that this condition is only sufficient if the differential operator of the delay free system generates a compact semigroup and the control space has a finite dimension.
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