Stability of Vector Differential Delay Equations

Michael I. Gil'

ISBN 10: 3034805764 / ISBN 13: 9783034805766

Verlag: Springer Basel, Birkhäuser Basel Feb 2013, 2013

Beschreibung

Neuware -Differential equations with delay naturallyarise 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 approachallows 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 functionsand 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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 272 pp. Englisch.

Bestandsnummer des Verkäufers 9783034805766

Bibliografische Details

• Titel: Stability of Vector Differential Delay Equations
• Verlag: Springer Basel, Birkhäuser Basel Feb 2013
• Erscheinungsjahr: 2013
• Sprache: Englisch
• ISBN-10: 3034805764
• ISBN-13: 9783034805766
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 240B x 168 H x 15 T Millimeter Breite: 240 mm, Höhe: 168 mm, Tiefe: 15 mm
• Gewicht: 462 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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