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Weakly Connected Nonlinear Systems - Boundedness and Stability of Motion (Hardcover)
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Weakly Connected Nonlinear Systems - Boundedness and Stability of Motion (Hardcover)
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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.
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