Electrical engines are widespread in all areas of industry and technology. Electrical actuators are widely used as an actuating motor regulating the interconnected controls of different machines. Increased demands for precision in interconnected controls make it very important to consider dry friction in the executive mechanism. The consideration of dry friction in a mathematical model of an automatic system considerably complicates its analysis. In all known practical cases of research into such issues, the research is carried out by means of computing or analytically, but using a considerably simplified model of the dry-friction law. This simplified presentation does not allow one to uncover and understand the true (or apparent) reasons for loss of stability in a system accompanied by friction self-oscillations of different kinds (periodical, chaotic etc.). The decomposition method of parameter space presented in the current work allows investigation of nonautonomous nonlinear multivariable systems via basic subsystems (both linear and nonlinear) that have a lower-order state space and are amenable to strict analysis.