During production flight tests, a number of aircrafts of different types and constructors have exhibited small and uncommanded yaw shudders or 'kicks' which in some instances were accompanied by minute, poorly damped oscillations.  In a continuation of a collaborative research study carried out by Concordia University and Bombardier Aerospace, this thesis aims to understand and eventually eliminate this phenomenon. Based on previous work done on a detailed flight model that concludes that the yaw 'kicks' are most likely initiated by uncommanded small deflections of the rudder, this thesis investigates the possibility that discontinuous non-linearities in the rudder control system might be at the root of the problem. The research in this study is conducted through modeling and virtual testing of the rudder control system, and are also aims at producing an "industrially viable" model.  The research involved the modeling of the system including various non-linearities, as well as the integration of the hydraulic servo actuators, concluding with the validation of the model. Finally, an extensive "trial-and-error" investigation was performed where variations of the non-linearities within realistic/actual tolerances were used to instantiate a number of different model configurations, each of them being virtually "flown". This thesis demonstrates that under certain condition, the system can self-initiate a rudder deflection of the order of magnitude expected