Instability of the control systems with non-stationary nonlinearities

Sailaubay S. Zhumatov

2017

Closed access Metadata (CSL-JSON)
DOI 10.1063/1.5000661
Data confidence 70 medium
How this score is calculated

It is built from checkable properties of the record itself: whether the article has a DOI, how many independent sources confirmed its data, whether the required fields are filled in, and how recent the latest confirmation is. Disagreement between sources and a missing identifier lower it. A value of 80 or above means the record was published without further checking; 60 to 79 means it is published at reduced confidence, with a manual check advisable. A record verified by an editor by hand is never pushed below 90 by a recalculation. This scores our data about the article, not the article itself.

Abstract

We study the inverse dynamics problem: for a given manifold restore a force field, which lies in the tangent subspace to manifold. This inverse problem is very important for a variety of mathematical models mechanics. We solve the problem of construction of differential equations’ system by given program manifold. This problem is reduced to investigation of quality properties of program manifold. The conditions of instability of the control systems with non-stationer nonlinearities are considered in the neighborhood of a program manifold. Nonlinearity satisfies conditions of local quadratic relations. The sufficient conditions of instability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function in the class of continuously-differentiable at time and bounded on a norm matrices.