Study of the Parameter Space of a Multidimensional Systemwith Relay Hysteresis and Perturbation

The object of study is an $$n$$ -dimensional system of ordinary differential equations containing 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 nonzero element), we obtain conditions on system parameters ensuring the existence of a unique two-point oscillatory periodic solution with period a multiple of the perturbation function period. We establish a functional dependence of the nonlinearity parameter on the perturbation function parameter. The influence of the perturbation function parameter values on the existence of the solution is studied. We suggest an algorithm for seeking system parameters and the instant of the first relay switching for the case in which the solution period is given. The theoretical results, including the proposed algorithm, are illustrated by an example of a three-dimensional system.