In this paper, the methods of the stability theory of differential equations with time delays are used in the study of an actual engineering problem of a drone (UAV) autonomous flight. We describe correct operation of autopilot for supply stability of desirable drone flight. There exists a noticeable delay in getting information about position and orientation of a drone to autopilot in the presence of vision-based navigation (visual navigation). In spite of this fact, we demonstrate that it is possible to provide stable flight at a constant height in a vertical plane. We describe how to form relevant controlling signal for autopilot in the case of the navigation information delay and provide control parameters for particular case of flight.

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