On Feedback Stabilizability of Linear Systems With State and Input Delays in Banach Spaces
Hadd, S.
Qing-Chang Zhong
Dept. of Electr. Eng. & Electron., Univ. of Liverpool, Liverpool;
This paper appears in: Automatic Control, IEEE Transactions on
Publication Date: March 2009
Volume: 54,
Issue: 3
On page(s): 438-451
ISSN: 0018-9286
INSPEC Accession Number: 10505310
Digital Object Identifier: 10.1109/TAC.2009.2012969
First Published: 2009-02-27
Current Version Published: 2009-03-10
Abstract
The feedback stabilizability of a general class of well-posed linear systems with state and input delays in Banach spaces is studied in this paper. Using the properties of infinite dimensional linear systems, a necessary condition for the feedback stabilizability of delay systems is presented, which extends the well-known results for finite dimensional systems to infinite dimensional ones. This condition becomes sufficient as well if the semigroup of the delay-free system is immediately compact and the control space is finite dimensional. Moreover, under the condition that the Banach space is reflexive, a rank condition in terms of eigenvectors and control operators is proposed. When the delay-free state space and control space are all finite dimensional, a very compact rank condition is obtained. Finally, the abstract results are illustrated with examples.
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