1 M.V. Lomonosov Moscow State University, Moscow, Russia
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Abstract. A simple and quick method is proposed for estimation of the asymptotic stability of highly nonlinear dynamic systems, in particular, of the high-dimensional systems for which Tailor series of the right-hand sides of the differential equations converge very slowly. In this case, the sum of terms of the order of smallness higher than two can substantially exceed the value of any term of second order. In this case, Lyapunov’s method cannot guarantee correct stability estimate. The new method is based on the procedure of maximization of the velocity of variation in metrics of the perturbed state space. This metrics can at the same time also be a Lyapunov function. The proposed new method is not intended for the stability estimate of linear systems.
Keywords: motion stability, nonlinear dynamic systems.