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Functional Differential Equations : Application of i-smooth calculus - Arkadii V. Kim

Functional Differential Equations

Application of i-smooth calculus

Hardcover Published: 31st May 1999
ISBN: 9780792356899
Number Of Pages: 168

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Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari­ fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional approach, different aspects of time-delay system theory have been developed with almost the same completeness as the corresponding field of ODE (ordinary differential equations) the­ ory. The term functional differential equations (FDE) is used as a syn­ onym for systems with delays 1. The systematic presentation of these re­ sults and further references can be found in a number of excellent books [2, 15, 22, 32, 34, 38, 41, 45, 50, 52, 77, 78, 81, 93, 102, 128]. In this monograph we present basic facts of i-smooth calculus ~ a new differential calculus of nonlinear functionals, based on the notion of the invariant derivative, and some of its applications to the qualitative theory of functional differential equations. Utilization of the new calculus is the main distinction of this book from other books devoted to FDE theory. Two other distinguishing features of the volume are the following: - the central concept that we use is the separation of finite dimensional and infinite dimensional components in the structures of FDE and functionals; - we use the conditional representation of functional differential equa­ tions, which is convenient for application of methods and constructions of i~smooth calculus to FDE theory.

`The book is warmly recommended for students and researchers in mathematics, applied mathematicians, and engineers whose work involves ordinary differential equations, functional analysis, partial equations, optimal control and mathematics system theory.' Acta Scientiarum Mathematicarum

Preface
i-Smooth Calculus
Structure of Functionals
Properties of Functionals. Invariant Derivative
Generalized Derivatives of Nonlinear Functionals
Functional Differential Equations
Functional Differential Equations
Neutral Functional Differential Equations
Direct Lyapunov Method for Systems with Delays
The Problem Statement
The Lyapunov Functional Method
The Lyapunov Function Method
Instability
Dynamical Programming Method for Systems with Delays
Systems with State Delays
Systems with Control Delays
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792356899
ISBN-10: 0792356896
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 168
Published: 31st May 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 17.15 x 26.04  x 1.27
Weight (kg): 0.45