Periodic Control System Stabilization on Time Scales

The stabilization of periodic control systems using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we suggest an alternative way to solve stabilization problems. This method is based on a combination of the Lyapunov functions method with local controllability conditions. In many situations this method admits a rigorous mathematical justification and leads to effective numerical methods. Applications to mechanical problems are provided here.