Martynyuk / Chernetskaya Weakly Connected Nonlinear Systems

Boundedness and Stability of Motion
1. Auflage 2013
ISBN: 978-1-4665-7087-0
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 228 Seiten

Reihe: Chapman & Hall/CRC Pure and Applied Mathematics

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.

Zielgruppe

Researchers and graduate students in mathematics, engineering, and physics.

Autoren/Hrsg.

Martynyuk, Anatoly

Chernetskaya, Larisa

Martynyuk, Vladislav

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.