On existence conditions for a two-point oscillating periodic solution in an non-autonomous relay system with a Hurwitz matrix

We consider a system of differential equations with relay nonlinearity and an external continuous periodic influence. For system parameters, we obtain sufficient existence and uniqueness conditions for a two-point oscillating solution with given period in case of a Hurwitz system matrix. With exact analytic approaches, we find time moments and switching points in the phase space of the image point for a solution whose period is a multiple of the period of external disturbances. We obtain conditions on system parameters for which a solution in the considered class is asymptotically-orbital stable.