Systems control with distributed parameters is one of the complex and important sections of cybernetics, like the science of control, information and systems. The need to study and develop this scientific discipline is due to the fact that to control many objects you have to take into account their geometric parameters, that is, their spatial length. So far, many results have been achieved in the field of distributed system theory, but for the most part these results are aimed at the study of linear systems. In the course of researching non-linear automatic systems, as one of the main tasks, the task of finding possible states of equilibrium of the system under study is solved. Research into the sustainability of such systems is also a major challenge. Using the technique of decomposition of functions that describe distributed signals in rows, according to the general theory of the Fourier series, a class of distributed systems is allocated, in which decomposition by its own vector functions is permissible. Due to this capability, the transmission function that describes an object with distributed parameters appears as a combination of transmission functions in separate spatial mods. The concept of "generalized coordinates" is introduced to take into account the spatial coordinates. For systems with distributed parameters, the spatialamplifier gain factor is adopted as a direct non-linear angular angular ratio. A cylindrical criterion for the absolute stability of non-linear distributed systems has been developed and formulated, based on the generalization of the circular criterion. An illustration of the spatial sector of nonlineaivity is given. For the first time, a generalized circular criterion for the stability of distributed systems has been developed, taking into account the dependence of non-linear characteristics on spatial coordinates. A graphic illustration of this criterion is presented.
