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

✍ Scribed by Heide Gluesing-Luerssen

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 183
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

3 The Algebraic Structure of H0
3.1 Divisibility Properties
3.2 Matrices over H0
3.3 Systems over Rings: A Brief Survey
3.4 The Nonfinitely Generated Ideals of H0
3.5 The Ring H as a Convolution Algebra
3.6 Computing the Bezout Identity
4 Behaviors of Delay-Differential Systems
4.1 The Lattice of Behaviors
4.2 Input/Output Systems
4.3 Transfer Classes and Controllable Systems
4.4 Subbehaviors and Interconnections
4.5 Assigning the Characteristic Function
4.6 Biduals of Nonfinitely Generated Ideals
5 First-Order Representations
5.1 Multi-Operator Systems
5.2 The Realization Procedure of Fuhrmann
5.3 First-Order Realizations for Delay-Differential Systems
5.4 Some Minimality Issues
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