Many problems in mechanics and technology lead to the study of nonstationary linear systems of ordinary differential equations, in particular, problems in the analysis of control systems and navigation of moving objects. To solve them successfully, effective, easy-to-use methods for studying processes occurring in non-stationary linear systems are required. It is required to find such control actions for a system of quadratic differential equations that ensure stability of the equilibrium position of the system over a finite period of time. In the article, a control of this type is obtained that stabilizes a system of quadratic differential equations of a certain type over a finite period of time.