On an output feedback finite-time stabilization problem

This note studies the problem of finite-time output feedback stabilization for the double integrator system. A class of output feedback controllers that fan achieve global finite-time stability for the double integrator system are constructed based on a "finite-time separation principle." Furthermore, it is shown that the closed-loop system resulting From our control law can maintain its total finite-time stability regardless of some nonlinear perturbations. Thus, our control law actually applies to a large class of nonlinear second order systems.