Nowadays, a natural consequence of intensive scientific and technological progress is the comprehensive complication of potential objects of management. For developers of automatic systems, this is primarily manifested in the fact that these objects in theory are characterized by a high order of the mathematical model, which often has significant nonlinearities or even variable parameters, and a very common class of nonlinearities of the “limiters” type deserves special mention, examples of which are “saturation", "rigid mechanical support" and other links implying a limitation on integration. In practice, this can often mean that it is impossible to obtain mathematical models of acceptable accuracy for such objects. For example, a large number of bench or field tests carried out in order to track the behavior of a complex and expensive technical complex is not always acceptable. The difficulty or impossibility of directly solving this problem is also supplemented by the pointlessness of such attempts due to the fact that such systems of differential equations would ideally describe only a specific object in a specific situation, which is explained by many random factors, ranging from the influence on the characteristics of the product of a set of initial conditions such as technological tolerances and errors, the use of qualitatively new materials, operating modes and ending with the influence of many external accidental influences on the operation of the product. In addition, for complex nonlinear mathematical models of a high order, approximation and linearization may not always be acceptable due to excessively high assumptions leading to strong differences in the real behavior of the object under control and the behavior predicted by theoretical calculations.