Weakly connected nonlinear systems : boundedness and stability of motion
- Martyni͡uk, A. A. (Anatoliĭ Andreevich)
- Boca Raton : CRC Press/Taylor & Francis Group, 
- Copyright notice
- Physical description
- xv, 212 pages : illustrations ; 24 cm.
- Monographs and textbooks in pure and applied mathematics ; 305.
QA871 .M344 2013
- Unknown QA871 .M344 2013
- Includes bibliographical references (pages 203-210) and index.
- 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 mu-Boundedness with Respect to Two Measures Boundedness and the Comparison Technique Boundedness with Respect to a Part of Variables Algebraic Conditions of mu-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 mu-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.
- (source: Nielsen Book Data)
- Publisher's 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.
(source: Nielsen Book Data)
- Publication date
- Copyright date
- Anatoly Martynyuk, Larisa Chernetskaya, Vladislav Martynyuk.
- Pure and applied mathematics ; 305
- "A Chapman & Hall book."