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

Format:

Book

Author/Creator:

Gluesing-Luerssen, Heide, 1961- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1770.

Lecture Notes in Mathematics, 0075-8434 ; 1770

Language:

English

Subjects (All):

Mathematical optimization.

Algebra.

Differential equations.

Calculus of Variations and Optimal Control; Optimization.

Ordinary Differential Equations.

Local Subjects:

Calculus of Variations and Optimal Control; Optimization.

Algebra.

Ordinary Differential Equations.

Physical Description:

1 online resource (X, 178 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2002.

System Details:

text file PDF

Summary:

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.

Contents:

Introduction

The Algebraic Framework

The Algebraic Structure of H_0. Divisibility Properties. Matrices over H_0. Systems over Rings: A Brief Survery. The Nonfinitely Generated Ideals of H_0. The Ring H as a Convolution Algebra. Computing the Bezout Identity

Behaviors of Delay-Differential Systems. The Lattice of Behaviors. Input/Output Systems. Transfer Classes and Controllable Systems. Subbehaviors and Interconnections. Assigning the Characteristic Function. Biduals of Nonfinitely Generated Ideals

First-Order Representations. Multi-Operator Systems. The Realization Procedure of Fuhrmann. First-Order Realizations. Some Minimality Issues.

Other Format:

Printed edition:

ISBN:

9783540455431

Access Restriction:

Restricted for use by site license.