Lyapunov-based approach for finite time stability and stabilization

Finite time stability is investigated for continuous system ẋ = f(x) which satisfies uniqueness of solutions in forward time. A necessary and sufficient condition is given for this class of systems using Lyapunov functions. Then, a necessary and sufficient condition is developed for finite time stabilization of class CL^k-affine systems involving a class CL⁰−settling time for the closed-loop system. Finally an explicit feedback control is given using a control Lyapunov function verifying a certain inequality.