Stability of vector differential delay equations
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 o...
Gardado en:
| Autor Principal: | |
|---|---|
| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado: |
Basel :
Springer Basel
[20..].
Cham : Springer Nature |
| Edición: | 1st ed. 2013. |
| Series: | Frontiers in Mathematics
|
| Acceso en liña: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Stability of vector differential delay equations, Michael I. Gil½, Basel, Birkhäuser, Springer [diffuseur], 2013, 1 vol. (X-259 p.), Frontiers in mathematics, 978-3-0348-0576-6 |
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| 100 | 1 | |a Gil', Mihail Iosifovič, |d 1941- | |
| 245 | 1 | 0 | |a Stability of vector differential delay equations |c by Michael I. Gil . |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a Basel : |b Springer Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Frontiers in Mathematics |x 1660-8054 | |
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Preface 1 Preliminaries 2 Some Results of the Matrix Theory 3 General Linear Systems 4 Time-invariant 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 Semi-Linear 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 776 | 0 | |0 168789116 |t Stability of vector differential delay equations |f Michael I. Gil½ |c Basel |n Birkhäuser |n Springer [diffuseur] |d 2013 |p 1 vol. (X-259 p.) |s Frontiers in mathematics |z 978-3-0348-0576-6 | |
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