Weakly Connected Nonlinear Systems: Boundedness and Stability of Motion

Anatoly Martynyuk, Larisa Chernetskaya, Vladislav Martynyuk

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November 20, 2012 by Chapman and Hall/CRC
Reference - 228 Pages
ISBN 9781466570863 - CAT# K16508
Series: Chapman & Hall/CRC Pure and Applied Mathematics

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Features

  • Presents the mathematical foundations of integral and differential inequalities, comparison techniques, the direct Lyapunov method, and stability definitions for systems with a small parameter
  • Covers recently developed approaches based on the direct Lyapunov method and the comparison technique for the investigation of the boundedness of motion of weakly connected nonlinear systems with two different measures
  • Examines the stability conditions of solutions of the weakly connected systems of differential equations based on the direct Lyapunov method and the comparison technique
  • Applies a general approach to the study of the stability of solutions for nonlinear systems with small perturbing forces
  • Describes fundamental results on the boundedness and stability of systems in Banach spaces with weakly connected subsystems

Summary

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.