Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion, 1st Edition (Hardback) book cover

Weakly Connected Nonlinear Systems

Boundedness and Stability of Motion, 1st Edition

By Anatoly Martynyuk, Larisa Chernetskaya, Vladislav Martynyuk

Chapman and Hall/CRC

228 pages

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Hardback: 9781466570863
pub: 2012-11-20
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Description

Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion provides a systematic study on the boundedness and stability of weakly connected nonlinear systems, covering theory and applications previously unavailable in book form. It contains many essential results needed for carrying out research on nonlinear systems of weakly connected equations.

After supplying the necessary mathematical foundation, the book illustrates recent approaches to studying the boundedness of motion of weakly connected nonlinear systems. The authors consider conditions for asymptotic and uniform stability using the auxiliary vector Lyapunov functions and explore the polystability of the motion of a nonlinear system with a small parameter. Using the generalization of the direct Lyapunov method with the asymptotic method of nonlinear mechanics, they then study the stability of solutions for nonlinear systems with small perturbing forces. They also present fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems through the generalization of the direct Lyapunov method, using both vector and matrix-valued auxiliary functions.

Designed for researchers and graduate students working on systems with a small parameter, this book will help readers get up to date on the knowledge required to start research in this area.

Table of Contents

Preliminaries

Introductory Remarks

Fundamental Inequalities

Stability in the Sense of Lyapunov

Comparison Principle

Stability of Systems with a Small Parameter

Analysis of the Boundedness of Motion

Introductory Remarks

Statement of the Problem

μ-Boundedness with Respect to Two Measures

Boundedness and the Comparison Technique

Boundedness with Respect to a Part of Variables

Algebraic Conditions of μ-Boundedness

Applications

Analysis of the Stability of Motion

Introductory Remarks

Statement of the Problem

Stability with Respect to Two Measures

Equistability via Scalar Comparison Equations

Dynamic Behavior of an Individual Subsystem

Asymptotic Behavior

Polystability of Motion

Applications

Stability of Weakly Perturbed Systems

Introductory Remarks

Averaging and Stability

Stability on a Finite Time Interval

Methods of Application of Auxiliary Systems

Systems with Nonasymptotically Stable Subsystems

Stability with Respect to a Part of Variables

Applications

Stability of Systems in Banach Spaces

Introductory Remarks

Preliminary Results

Statement of the Problem

Generalized Direct Lyapunov Method

μ-Stability of Motion of Weakly Connected Systems

Stability Analysis of a Two-Component System

Bibliography

Index

Comments and References appear at the end of each chapter.

About the Series

Chapman & Hall/CRC Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI055000
SCIENCE / Physics