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Volume 5, Issue 6, December 2019, Page: 113-117
Simple and Effective Theory of Movement Steadiness
Smol’yakov Eduard Rimovich, Department of Mathematics, Lomonosov Moscow State University, Moscow, Russia
Received: Nov. 10, 2019;       Accepted: Dec. 2, 2019;       Published: Dec. 11, 2019
Abstract
It is proposed the very simple and quick method for estimation of the asymptotic stability of any 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 such problems, 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 methods cannot guarantee correct stability estimate at all. The new method does not use the notion of Liapunov function and, therefore, one has no numerous shortcomings of all Liapunov methods. In this paper, it is proposed to replace the very complex problem of the searching for Liapunov function with a very simple problem of the searching maximum of the function of n coordinates (that is of the velocity of variation in metrics of the perturbed state space). However, one is not intended for the linear systems.
Keywords
Nonlinear Dynamical Systems, Movement Steadiness, New Theory
Smol’yakov Eduard Rimovich, Simple and Effective Theory of Movement Steadiness, International Journal of Theoretical and Applied Mathematics. Vol. 5, No. 6, 2019, pp. 113-117. doi: 10.11648/j.ijtam.20190506.15
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