Frontiers in Mathematics

Stability of Vector Differential Delay Equations

Authors: Gil’, Michael I.

  • ​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  
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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.

About the authors

Michael I. Gil' is professor of mathematics at Ben Gurion University of the Negev in Beer Sheva, Israel.

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)

Table of contents (14 chapters)

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-0348-0577-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-0348-0576-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Stability of Vector Differential Delay Equations
Authors
Series Title
Frontiers in Mathematics
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
eBook ISBN
978-3-0348-0577-3
DOI
10.1007/978-3-0348-0577-3
Softcover ISBN
978-3-0348-0576-6
Series ISSN
1660-8046
Edition Number
1
Number of Pages
X, 259
Topics