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

  • Book
  • © 2002

Overview

Authors:
  1. Heide Gluesing-Luerssen
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1770)

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Table of contents (7 chapters)

  1. Front Matter

    Pages N2-VII
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  2. 1. Introduction

    • Heide Gluesing-Luerssen
    Pages 1-5

  3. 2. The Algebraic Framework for Delay-Differential Equations

    • Heide Gluesing-Luerssen
    Pages 7-21

  4. 3. The Algebraic Structure of

    • Heide Gluesing-Luerssen
    Pages 23-72

  5. 4. Behaviors of Delay-Differential Systems

    • Heide Gluesing-Luerssen
    Pages 73-134

  6. 5. First-Out Representations

    • Heide Gluesing-Luerssen
    Pages 135-167

  7. References

    • Heide Gluesing-Luerssen
    Pages 169-174

  8. Subject Index and Notation Index

    • Heide Gluesing-Luerssen
    Pages 175-176

  9. Back Matter

    Pages 177-177
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Keywords

About this book

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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