Stability of vector differential delay equations
 Author/Creator
 Gilʹ, M. I. (Mikhail Iosifovich)
 Language
 English.
 Imprint
 Basel ; New York : Birkhäuser, c2013.
 Physical description
 x, 259 p. : ill. ; 24 cm.
 Series
 Frontiers in mathematics.
Access
Available online

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QA371 .G55 2013

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QA371 .G55 2013
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Contents/Summary
 Bibliography
 Includes bibliographical references (p. 249255) and index.
 Contents

 Preface. 1 Preliminaries. 2 Some Results of the Matrix Theory. 3 General Linear Systems. 4 Timeinvariant Linear Systems with Delay. 5 Properties of Characteristic Values. 6 Equations Close to Autonomous and Ordinary Differential Ones. 7 Periodic Systems. 8 Linear Equations with Oscillating Coefficients. 9 Linear Equations with Slowly Varying Coefficients. 10 Nonlinear Vector Equations. 11 Scalar Nonlinear Equations. 12 Forced Oscillations in Vector SemiLinear Equations. 13 Steady States of Differential Delay Equations. 14 Multiplicative Representations of Solutions. Appendix A. The General Form of Causal Operators. Appendix B. Infinite Block Matrices. Bibliography. Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 inputtostate 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 wellknown 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 matrixvalued functions and the following methods and results: the generalized BohlPerron principle and the integral version of the generalized BohlPerron principle; the freezing method; the positivity of fundamental solutions. A significant part of the book is devoted to the AizermanMyshkis 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.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 Michael I. Gilʹ.
 Series
 Frontiers in mathematics
 ISBN
 3034805764
 9783034805766 (pbk.)