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Applications of Liapunov Methods in Stability (Paperback, Softcover reprint of the original 1st ed. 1993)
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Applications of Liapunov Methods in Stability (Paperback, Softcover reprint of the original 1st ed. 1993)
Series: Mathematics and Its Applications, 245
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The year 1992 marks the centennial anniversary of publication of
the celebrated monograph "The General Problem of Stability of
Motion" written by A. M. Liapunov. This anniversary inspires to
think about the way theory and applications have developed during
this century. The first observation one can make is that the
so-called "second method," nowadays known as the "Liapunov function
method," has received more attention than the "first method"; let
us also mention the study of critical cases, which brought more
attention recently in connection with the study of bifurcations and
with nonlinear stabilization. One of the reasons of popularity of
the Liapunov function approach might be the fact that, in many
situations in science and engineering, and not only in mechanics,
which was the main source of inspiration for the work of Liapunov,
natural Liapunov functions may be proposed, intimately connected
with the properties of the processes. It is one of the purposes of
this book to advocate this idea. From the mathematical viewpoint,
the century after the first appear ance of Liapunov's monograph has
been characterized both by general izations and by refinements of
Liapunov's ideas. But we feel that the most spectacular progress is
the understanding of the wide possibilities open for applications
by the use of Stability Theory as constructed by Liapunov a century
ago. We have tried to show some of the ideas in this direction by
start ing with our personal experience in the study of some
models."
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