Introduction to the Theory and Applications of Functional Differential Equations
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...
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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. 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. Booknews 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)
PrefacePt. IModelling by Functional Differential EquationsCh. 1Theoretical preliminariesCh. 2ModelsPt. IITheoretical Background of Functional Differential EquationsCh. 3General theoryPt. IIIStabilityCh. 4Stability of retarded differential equationsCh. 5Stability of RDEs with autonomous linear partCh. 6Liapunov functionals for concrete FDEsCh. 7Riccati type stability conditions of some linear systems with delayCh. 8Stability of neutral type functional differential equationsCh. 9Applications of the direct Liapunov methodCh. 10Stability of stochastic functional differential equationsPt. IVBoundary Value Problems and Periodic Solutions of Differential EquationsCh. 11Boundary value problems for functional differential equationsCh. 12Fredholm alternative for periodic solutions of linear FDEsCh. 13Generalized periodic solutions of functional differential equationsPt. VControl and Estimation in Hereditary SystemsCh. 14Problems of control for deterministic FDEsCh. 15Optimal control of stochastic delay systemsCh. 16State estimates of stochastic systems with delayBibliographyIndex
\ BooknewsCovering 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)\ \
