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On the problem of the stability of a motion. (English. Russian original) Zbl 1060.34505
Autom. Remote Control 61, No. 4, Part 1, 585-594 (2000); translation from Avtom. Telemekh. 2000, No. 4, 51-60 (2000).
Summary: The problem of constructing the ideal triple: “metric – pilot function – vector field” for a given dynamical system is considered. Properties of the triple are studied, and the notion of the (ideal) Lyapunov function for the given dynamical system is introduced. This notion allows one to construct the Lyapunov function directly by the right-hand side of the given differential equation.

MSC:
34C20 Transformation and reduction of ordinary differential equations and systems, normal forms
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