When studying various processes taking place in real life, we have to deal with one of the most important concepts -
the concept of stability of movement. The foundations of the theory of stability of motion were developed at the end of
the last century by the great Russian scientist A. M. Lyapunov. As is known, Lyapunov stability is considered on an
infinite time interval, which is a serious obstacle for many applications, since most of the objects of research function for
a finite period of time. The concept of stability, introduced for an unlimited period of time, cannot be used to evaluate the
properties of motion within a finite period of time. The study of motion stability by analyzing solutions of the
corresponding equations is permissible and makes sense only if the mathematical model of physical reality is fully
adequate. The purpose of this work is to study the stability and stabilization of the motion of linear non-stationary systems.