Application of Popov´s criterion to signal stabilization in discrete systems

In a previous paper [1], a new method called the dual input discrete describing function (DIDDF) was presented, which enables one to determine the minimum amplitude of sinusoidal dither to be applied, to stabilize a relay type sampled-data control system. In this correspondence Popov´s method is used to find the minimum amplitude of the dither to be applied to quench the limit cycles occurring in relay type nonlinear control systems. Furthermore, the dependence of the minimum value of the dither on sampling time is explicitly seen in Popov´s method.