Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion, 1st Edition (Paperback) 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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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. Analysis of the Boundedness of Motion. Analysis of the Stability of Motion. Stability of Weakly Perturbed Systems. Stability of Systems in Banach Spaces. Bibliography. Index.

About the Authors

Martynyuk, Anatoly; Chernetskaya, Larisa; Martynyuk, Vladislav

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
SCI055000
SCIENCE / Physics