On some method of calming down mechanical system with aftereffect

The differential equation of the mathematical model of a vertical triangle is studied, the right side of which contains terms with a linear delay. The equation under study is of a neutral type. Such equations are found in the fields of mechanics, biology, and economics. The problem of stabilization of this controlled mathematical model is investigated. The system contains two linear delays. Since these delays increase at $t\to\infty$, stabilization is performed over an infinite period of time $t$. The calming of a system that does not contain neutral terms in the right part is performed using the stabilization algorithm proposed for ordinary differential equations. For further stabilization, the algorithm of stabilization of difference systems is used. A specific numerical example is given and a search for numerical solutions to the equations obtained in the stabilization process is carried out. A package MatLab of applied problems was used to solve Lyapunov type equations and numerically calculate solutions.