On the construction of Lyapunov's function

The problem of stability of the system of non-linear stationary differential equations is considered when perturbating forces of small integral act on the system during finite time interval. By means of Lyapunov’s functions necessary and sufficient conditions have been obtained for linear stationary systems in case of which the system is stable for any acting forces [1]. The sufficient conditions in case of which the non-linear system is stable for any acting forces have been defined. A concrete example has been constructed where the system becomes instable when the mentioned conditions are not kept.