Using the theory of hyperstability, an adaptive control system of DC motor speed is developed, which: 1) uses only measurable signals; 2) takes into account the boundedness of the control action signal; 3) compensates for the negative effect of the non-stationarity of the inertia moment and load torque on the quality of speed control. A mathematical proof of the asymptotic hyperstability of the developed system is derived using the second Lyapunov method and Popov's criterion. The numerical experiments are conducted. They demonstrate that the developed system effectively compensates for the wide-range variations of the load torque and motor inertia moment. Such range is enough for practical needs.