Abstract
The object of study is an \(n\) -dimensional systemof ordinary differential equations containing a constant diagonal matrix with real eigenvalues,two-position relay nonlinearity of hysteresis type with a parameter, and a continuous periodicperturbation function with a parameter. In the case of a special type of feedback vector (onenonzero element), we obtain conditions on system parameters ensuring the existence of a uniquetwo-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 functionparameter. The influence of the perturbation function parameter values on the existence of thesolution is studied. We suggest an algorithm for seeking system parameters and the instant of thefirst 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.
