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

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This book covers the most important issues in the theory of functional differential equations and their applications for both deterministic and stochastic 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.
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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 (
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Product Details

  • ISBN-13: 9780792355045
  • Publisher: Springer Netherlands
  • Publication date: 1/31/1999
  • Series: Mathematics and Its Applications (closed) Series, #463
  • Edition description: 1999
  • Edition number: 1
  • Pages: 648
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.50 (d)

Table of Contents

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