Linear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach
The book deals with linear time-invariant delay-differential equations with commensurated point delays in a control-theoretic context. The aim is to show that with a suitable algebraic setting a behavioral theory for dynamical systems described by such eq
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1770
Springer Berlin Heidelberg New York Barcelona Hong Kong London Milan Paris Singapore Tokyo
Heide
Gluesing-Luerssen,
Linear
Delay- Differential
Systems with
Delays: An Algebraic Approach Commensurate
4
11,11 4%
Springer
Author Heide
Gluesing-Luerssen
Department of Mathematics University of Oldenburg 26111 Oldenburg, Germany e-mail:
[email protected]
Cataloging-in-Publication Data available Die Deutsche Bibliothek
-
CIP-Einheitsaufnahme
Gltising-Ltierssen, Heide: delay differential systernswith commensurate'delays : an algebraic approach / Heide Gluesing-Lueerssen. Berlin; Heidelberg; New York; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Tokyo : Springer, 2002 (Lecture notes in mathematics ; 1770) Linear
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ISBN 3-540-42821-6
Mathematics
Subject Classification (2000): 93CO5, 93B25, 93C23, 13B99, 39B72
ISSN 0075-8434 ISBN 3-540-42821-6
Springer-Verlag Berlin Heidelberg New York
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Preface
delay-differential equation was coined to comprise all types of differequations in which the unknown function and its derivatives occur with
The term ential
various values of the argument. In these notes we concentrate on (implicit) linear delay-differential equations with constant coefficients and commensurate
point delays. We present
an
investigation of dynamical delay-differential
sys-
tems with respect to their general system-theoretic properties. To this end, an algebraic setting for the equations under consideration is developed. A thorough
purely algebraic study shows that this setting is well-suited for an examination of delay-differential systems from the behavioral point of view in modern systems theory. The central object is a suitably defined operator algebra which turns out to be an elementary divisor domain and thus provides the main tool for handling matrix equations of delay-differential
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