Control design for a perturbed system with an ambiguous nonlinearity

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.