Finite time stability and stabilization of a class of continuous systems

Finite time stability is investigated for continuous system ˙x = f (x) which satisfies uniqueness of solutions in forward time. A necessary and sufficient condition for finite time stability is given for this class of systems using Lyapunov functions. Then, a necessary and sufficient condition is developed for finite time stabilization of class CLk-affine systems ˙x = f (x) + g(x)u involving a class CL0-settling-time function for the closed-loop system. Finally an explicit feedback control is addressed by using a control Lyapunov function verifying a certain inequality. © 2005 Elsevier Inc. All rights reserved.