The partial stability of motion / Vorotnikov V.I. // Journal of Applied Mathematics and Mechanics. - 1988. - V. 52, l. 3. - P. 289-300.

ISSN:
00218928
Type:
Article
Abstract:
It is proved that the problem of stability (asymptotic stability) with respect to some of the variables, for a linear system with periodic analytic coefficients, is equivalent to the same problem with respect to all the variables, either for the same system or for an auxiliary linear system with periodic but not necessarily continuous coefficients, in less dimensions than the original system. A constructive procedure is described for constructing this auxiliary system, and the necessary and sufficient conditions are established for partial stability (asymptotic stability), generalizing the results of the Floquet-Lyapunov theory. It is shown that the class of non-linear systems for which the problem of partial stability is solvable by linear approximation may be enlarged if, instead of the linear part of the original (non-linear) system, one considers a specially constructed linear approximating system which is equivalent to a certain non-linear subsystem of the original system. Constructive procedures are described for constructing such auxiliary systems, and a theorem on partial stability is proved. Well-known theorems on stability in the Lyapunov-critical cases are extended. © 1989.
Author keywords:
Index keywords:
Mathematical Techniques--Differential Equations; Mechanics; System Stability; Asymptotic Stability; Floquet-Lyapunov Theory; Non-Linear Systems; Partial Stability of Motion; Periodic Coefficients; Equ
DOI:
10.1016/0021-8928(88)90080-9
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CODEN JAMMA
Language of Original Document English
Abbreviated Source Title J. Appl. Math. Mech.
Source Scopus