Overview
- The book provides Matlab codes and relevant descriptions to allow the interested reader to test and apply the proposed approaches in a practical perspective
- The book represents a self-contained treatment of the problem, from the theoretical aspects of the models to the practical computation of the results, passing through the numerical analysis of the proposed algorithms
- Presents the authors recent work on the numerical methods for the stability analysis of equilibria and periodic solutions
- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Electrical and Computer Engineering (BRIEFSELECTRIC)
Part of the book sub series: SpringerBriefs in Control, Automation and Robotics (BRIEFSCONTROL)
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Table of contents (8 chapters)
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Front Matter
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Numerical Analysis
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Front Matter
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Implementation and Applications
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Front Matter
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Back Matter
Keywords
- Asymptotic Stability
- Characteristic Equation, Roots and Multipliers
- Equilibria and Periodic Solutions
- Infinite Dimensional Dynamical Systems
- Matlab Codes
- Numerical Stability Analysis
- Pseudospectral and Collocation Methods
- Retarded Functional and Delay Differential Equations
- Semigroup of Solution Operators and Infinitesimal Generator
- Spectrum of Linear Operators and Eigenvalue Problems
- Time-delay models
About this book
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.
Authors and Affiliations
Bibliographic Information
Book Title: Stability of Linear Delay Differential Equations
Book Subtitle: A Numerical Approach with MATLAB
Authors: Dimitri Breda, Stefano Maset, Rossana Vermiglio
Series Title: SpringerBriefs in Electrical and Computer Engineering
DOI: https://doi.org/10.1007/978-1-4939-2107-2
Publisher: Springer New York, NY
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Author(s) 2015
Softcover ISBN: 978-1-4939-2106-5Published: 21 October 2014
eBook ISBN: 978-1-4939-2107-2Published: 21 October 2014
Series ISSN: 2191-8112
Series E-ISSN: 2191-8120
Edition Number: 1
Number of Pages: XI, 158
Number of Illustrations: 24 b/w illustrations, 1 illustrations in colour
Topics: Systems Theory, Control, Numerical Analysis, Control and Systems Theory