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Stability of Motion
$15.88
N. N. Krasovskii
Book
Stability of Motion
$15.88
N. N. Krasovskii
Book
This rigorous analysis extends the fundamental work of Lyapunov and applies his direct method to a variety of problems. Lyapunov's theorems on asymptotic stability and instability are generalized; the problems of mth-order stability and persistent disturbances and related questions are also explored. Extremely general results are established for differential systems with and without delay. Complete proofs of the main results are given; the weakest possible known hypotheses under which the theorems remain valid are indicated. Special emphasis is placed on theorems which have valid converses. The existence of Lyapunov functions which are periodic and very smooth is demonstrated. Lyapunov functions are applied to systems having the particular trajectory as a parameter, and to differential systems involving a set of parameters. One section deals with the theory and applications of the second method to differential equations with delay. By applying the general theory of semigroups to the family of trajectories, the author has been able to use a powerful method and obtain a well-rounded theory. When the Russian edition (1959) was published, Mathematical Reviews commented, "Highly interesting and valuable...The author is indeed one of the major and most original contributors to this general theory. The problems are constantly elucidated with clarity, the definitions are given in full, and most proofs are dealt with completely unless they are standard and readily accessible." Mr. Krasovskii is Professor of Mathematics at the S.M. Kirov Ural Polytechnical Institute, Sverdlovsk, R.F.S.F.R. Mr. Brenner is a Senior Mathematician at Stanford Research Institute. This is a reproduction edition from a scanned copy of the following original edition: Stability of motion: applications of Lyapunov's second method to differential systems and equations with delay N. N. Krasovskii, J L Brenner Stanford U.P., 1963 Find more reproduction works from Stanford University Press at QOOP.com
