Linear Delay-Differential Systems with Commensurate Delays: An Algebraic Approach

Heide Gluesing-Luerssen (auth.)3540428216, 9783540428213

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 equations can be developed. The central object is an operator algebra which turns out to be an elementary divisor domain and thus provides the main tool for investigating the corresponding matrix equations. The book also reports the results obtained so far for delay-differential systems with noncommensurate delays. Moreover, whenever possible it points out similarities and differences to the behavioral theory of multidimensional systems, which is based on a great deal of algebraic structure itself. The presentation is introductory and self-contained. It should also be accessible to readers with no background in delay-differential equations or behavioral systems theory. The text should interest researchers and graduate students.

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Table of contents :
1. Introduction….Pages 1-5
2. The Algebraic Framework for Delay-Differential Equations….Pages 7-21
3. The Algebraic Structure of $mathcal{H}_0$ ….Pages 23-72
4. Behaviors of Delay-Differential Systems….Pages 73-134
5. First-Out Representations….Pages 135-167
References….Pages 169-174
Subject Index and Notation Index….Pages 175-176