Stability of the asymptotic quiescent position of perturbed homogeneous nonstationary systems

Sufficient conditions for the existence of an asymptotic quiescent position for homogeneous non-stationary systems of ordinary differential equations with perturbations in the form of functions that disappear with time are obtained in this article. The method of proof is based on the construction of the Lyapunov function, which satisfies the conditions of the theorem proved by V. I. Zubov for the existence of an asymptotic quiescent position. An example of a system of non-linear and non-stationary ordinary differential equations is considered, which illustrates the obtained results.