Stability of Linear Delay Differential Equations: A Numerical Approach with MATLAB

✍ Scribed by Dimitri Breda, Stefano Maset, Rossana Vermiglio (auth.)

Publisher: Springer-Verlag New York
Year: 2015
Tongue: English
Leaves: 162
Series: SpringerBriefs in Electrical and Computer Engineering - SpringerBriefs in Control, Automation and Robotics
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

This book presents the authors' recent work on the numerical methods for the stability analysis of linear autonomous and periodic delay differential equations, which consist in applying pseudospectral techniques to discretize either the solution operator or the infinitesimal generator and in using the eigenvalues of the resulting matrices to approximate the exact spectra. The purpose of the book is to provide a complete and self-contained treatment, which includes the basic underlying mathematics and numerics, examples from population dynamics and engineering applications, and Matlab programs implementing the proposed numerical methods. A number of proofs is given to furnish a solid foundation, but the emphasis is on the (unifying) idea of the pseudospectral technique for the stability analysis of DDEs. It is aimed at advanced students and researchers in applied mathematics, in dynamical systems and in various fields of science and engineering, concerned with delay systems. A relevant feature of the book is that it also provides the Matlab codes to encourage the readers to experience the practical aspects. They could use the codes to test the theory and to analyze the performances of the methods on the given examples. Moreover, they could easily modify them to tackle the numerical stability analysis of their own delay models.

✦ Table of Contents

Front Matter....Pages i-xi
Introduction....Pages 1-14
Front Matter....Pages 15-16
Notation and Basics....Pages 17-21
Stability of Linear Autonomous Equations....Pages 23-33
Stability of Linear Periodic Equations....Pages 35-41
Front Matter....Pages 43-44
The Infinitesimal Generator Approach....Pages 45-65
The Solution Operator Approach....Pages 67-86
Front Matter....Pages 87-87
MATLAB Implementation....Pages 89-116
Applications....Pages 117-145
Back Matter....Pages 147-158

✦ Subjects

Systems Theory, Control; Numerical Analysis; Control

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