Overview
- Well-written systematic and comprehensive exposition
- Presents a solution of the Aizerman - Myshkis problem
- Develops the Hill method for functional differential equations with period coefficients
- Includes supplementary material: sn.pub/extras
Part of the book series: Frontiers in Mathematics (FM)
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology, learning models, epidemiology, physiology, and many others. This book systematically investigates the stability of linear as well as nonlinear vector differential equations with delay and equations with causal mappings. It presents explicit conditions for exponential, absolute and input-to-state stabilities. These stability conditions are mainly formulated in terms of the determinants and eigenvalues of auxiliary matrices dependent on a parameter; the suggested approach allows us to apply the well-known results of the theory of matrices. In addition, solution estimates for the considered equations are established which provide the bounds for regions of attraction of steady states.
The main methodology presented in the book is based on a combined usage of the recent norm estimates for matrix-valued functions and the following methods and results: the generalized Bohl-Perron principle and the integral version of the generalized Bohl-Perron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the Aizerman-Myshkis problem and generalized Hill theory of periodic systems.
The book is intended not only for specialists in the theory of functional differential equations and control theory, but also for anyone with a sound mathematical background interested in their various applications.
Reviews
From the reviews:
“This research monograph presents and studies the stability of linear and nonlinear delay systems. … Every chapter begins with a brief description of its contents and is completed by ‘Comments’ with some remarks and references. … the book contains many interesting results on stability analysis and can be recommended to specialists in linear stability theory and researchers interested by analysis of delay systems.” (Nataliya Olegovna Sedova, Mathematical Reviews, November, 2013)Authors and Affiliations
About the author
Bibliographic Information
Book Title: Stability of Vector Differential Delay Equations
Authors: Michael I. Gil’
Series Title: Frontiers in Mathematics
DOI: https://doi.org/10.1007/978-3-0348-0577-3
Publisher: Birkhäuser Basel
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Basel 2013
Softcover ISBN: 978-3-0348-0576-6Published: 26 February 2013
eBook ISBN: 978-3-0348-0577-3Published: 14 February 2013
Series ISSN: 1660-8046
Series E-ISSN: 1660-8054
Edition Number: 1
Number of Pages: X, 259
Topics: Ordinary Differential Equations, Systems Theory, Control, Applications of Mathematics