Unmanned aerial vehicles are by far the most promising military and civilian systems. There is a tendency to increase the efforts of a number of leading countries in the development of unmanned aerial vehicles and their complexes. The mathematical model of any system reflects in one way or another its real properties, including the existing limitations. It has been found that one of the most favorable and efficient methods for constructing mathematical models of automatic control systems is to

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... evelop them using transfer functions. In order to solve this problem, the article deals with the composition of the control system of a drone. A mathematical model consisting of the joint design of the unmanned aerial vehicle and its automatic control system has been synthesized. The description of the proposed mathematical model of the system is based on the representation of a linear continuous system by the difference equations obtained using the Tustin relation. The mathematical model proposed in the article can be used for the study of typical aircraft whose course management system is built according to the considered structure. The practical significance of the obtained results is the possibility of applying the developed mathematical model to study the dynamics of the change of state and to set up the system of automatic control of the course of the unmanned aerial vehicle through computer simulation. Prospects for further research in this area are computer simulation of an unmanned aerial vehicle control system and estimation of the accuracy of the mathematical model developed.