Introduction to the Theory and Applications of Functional Differential Equations / Edition 1

by V. Kolmanovskii, A. Myshkis

Overview

This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and shastic cases. Among the subjects treated are qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. The work, which treats many concrete problems in detail, gives a good overview of the entire field and will serve as a stimulating guide to further research.
Audience: This volume will be of interest to researchers and (post)graduate students working in analysis, and in functional analysis in particular. It will also appeal to mathematical engineers, industrial mathematicians, mathematical system theoreticians and mathematical modellers.

Product Details

ISBN-13:	9789048151486
Publisher:	Springer Netherlands
Publication date:	12/07/2010
Series:	Mathematics and Its Applications , #463
Edition description:	Softcover reprint of the original 1st ed. 1999
Pages:	648
Product dimensions:	6.10(w) x 9.25(h) x 0.06(d)

Table of Contents

I. Modelling by Functional Differential Equations.- 1. Theoretical preliminaries.- 2. Models.- II. Theoretical Background of Functional Differential Equations.- 3. General theory.- III. Stability.- 4. Stability of retarded differential equations.- 5. Stability of RDEs with autonomous linear part.- 6. Liapunov functionals for concrete FDEs.- 7. Riccati type stability conditions of some linear systems with delay.- 8. Stability of neutral type functional differential equations.- 9. Application of the direct Liapunov method.- 10. Stability of shastic functional differential equations.- IV. Boundary Value Problems and Periodic Solutions of Differential Equations.- 11. Boundary value problems for functional differential equations.- 12. Fredholm alternative for periodic solutions of linear FDEs.- 13. Generalized periodic solutions of Functional Differential Equations.- V. Control and Estimation in Hereditary Systems.- 14. Problems of control for deterministic FDEs.- 15. Optimal control of shastic delay systems.- 16. State estimates of shastic systems with delay.

Editorial Reviews

Covering the significant issues in the theory of functional differential equations (FDEs) and their applications for both deterministic and stochastic cases, this volume covers qualitative theory, stability, periodic solutions, optimal control and estimation, the theory of linear equations, and basic principles of mathematical modelling. A substantial overview of the field is provided, with many problems treated in considerable detail. The authors aim to provide a readable account of the newest developments in FDE theory and provide new material on the following areas: phenomena modelling by FDEs; boundary value problems; formal procedure for Liapunov functionals construction for different classes of FDEs; non-autonomous equations of first and second orders; minimax filtering and estimation; and model reference adaptive control. Of likely use to researchers and postgraduate students, as well as other users of FDEs. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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