Problems of control and stability of solutions to systems of differential equations for describing processes defined for linear operations are considered. This makes it possible to identify important properties inherent in all systems of the same class. For a structurally linear system that describes with a sufficient degree of accuracy the behavior of a system with transistor switches, the problem of constructing self-oscillations is considered. A qualitative study of the behavior of the system when choosing a control is carried out and a control is constructed under which self-oscillation occurs in the system.