STUDY OF PARAMETER SPACE OF MULTIDIMENSIONAL SYSTEM WITH RELAY HYSTERESIS AND PERTURBATION

The object of research is an 𝑛-dimensional system of ordinary differential equations that contains a constant diagonal matrix with real eigenvalues, two-position relay nonlinearity of hysteresis type with a parameter and a continuous periodic perturbation function with a parameter. In the case of a special type of feedback vector (one non-zero element), we obtain conditions for system parameters that ensure the existence of a unique two-point oscillatory periodic solution with a period multiple of the perturbation function period. We establish a functional dependence of the nonlinearity parameter on the perturbation function parameter. Influence of perturbation function parameter values on the existence of the solution is investigated. We offer an algorithm for seeking system parameters and the instant of the first relay switching in the case when the solution period is given. Theoretical results, including the proposed algorithm, are illustrated by the example of a three-dimensional system.