Prescribed Finite-Time Stabilization For Flat Systems

Prescribed finite-time stabilization is introduced in a systematic manner based on time-scale transformations. A class of linear time-varying differential equations with prescribed finite-time stability of the origin is derived via pole placement in the transformed time. An explicit parametrization of the general solution is presented. Prescribed finite-time stable dynamics are then used as target systems for flatness-based tracking control. The resulting inputs remain bounded and satisfy smoothness requirements. The control strategy shows inherent robustness against model uncertainties.