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

✍ Scribed by Heide Gluesing-Luerssen

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 181
• Edition: 1
• 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

9fm45heq2tqrnhtn.pdf......Page 0
3 The Algebraic Structure of $H_o$......Page 29
3.1 Divisibility Properties......Page 31
3.2 Matrices over $H_o$......Page 41
3.3 Systems over Rings: A Brief Survey......Page 49
3.4 The Nonfinitely Generated Ideals of $H_o$......Page 51
3.5'The Ring $H$ as a Convolution Algebra......Page 57
3.6 Computing the Bezout Identity......Page 65
4 Behaviors of Delay-Differential Systems......Page 79
4.1 The Lattice of Behaviors......Page 82
4.2 Input/Output Systems......Page 95
4.3 Transfer Classes and Controllable Systems......Page 101
4.4 Subbehaviors and Interconnections......Page 110
4.5 Assigning the Characteristic Function......Page 121
4.6 Biduals of Nonfinitely Generated Ideals......Page 135
5 First-Order Representations......Page 141
5.1 Multi-Operator Systems......Page 144
5.2 The Realization Procedure of Fuhrmann......Page 154
5.3 First-Order Realizations for Delay-Differential Systems......Page 163
5.4 Some Minimality Issues......Page 168