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

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

An Algebraic Approach

By: Heide Gluesing-Luerssen, H. Gluesing-Luerssen

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Paperback | 1 December 2001

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188 Pages

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23.5 x 15.24 x 1.27

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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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Introduction	p. 1
The Algebraic Framework	p. 7
The Algebraic Structure of H[subscript 0]	p. 23
Divisibility Properties	p. 25
Matrices over H[subscript 0]	p. 35
Systems over Rings: A Brief Survey	p. 43
The Nonfinitely Generated Ideals of H[subscript 0]	p. 45
The Ring H as a Convolution Algebra	p. 51
Computing the Bezout Identity	p. 59
Behaviors of Delay-Differential Systems	p. 73
The Lattice of Behaviors	p. 76
Input/Output Systems	p. 89
Transfer Classes and Controllable Systems	p. 95
Subbehaviors and Interconnections	p. 104
Assigning the Characteristic Function	p. 115
Biduals of Nonfinitely Generated Ideals	p. 129
First-Order Representations	p. 135
Multi-Operator Systems	p. 138
The Realization Procedure of Fuhrmann	p. 148
First-Order Realizations	p. 157
Some Minimality Issues	p. 162
Reference	p. 169
Index	p. 175
Table of Contents provided by Blackwell. All Rights Reserved.

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

An Algebraic Approach

At a Glance

Paperback

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