Existence of the unique kT-periodic solution for one class of nonlinear systems

The system of ordinary differential equations with the discontinuous hysteresic nonlinearity and an external continuous biharmonic influence is considered. Sufficient conditions are obtained for existence of periodic solutions with given properties, in particular, with the period equal and multiple to the period of the external influence. We use an approach to the choice of feedback coefficients based on a nonsingular transformation of the initial system to a special canonical form. The approach allows to find analytically the switching instants and points of the image point of the required solution.