—The object of this study is an n-dimensional system of ordinary differential equations
with an ambiguous relay nonlinearity under a continuous periodic perturbation. We consider
continuous periodic solutions of the system with the state-space trajectory consisting of two
parts connected at relay switching points. We develop an algorithm for selecting the nonlinearity
parameters under which there is a unique asymptotically orbitally stable periodic solution of
the system with given oscillation properties, including a given period and two switching points
per period.