International audienceLyapunov characterizations of output finite-time stability are presented for the system x′=f(x),y=h(x) which is locally Lipschitz continuous out of the set Y=x∈Rn:h(x)=0 and continuous on Rn. The definitions are given in the form of K and KL functions. Necessary and sufficient conditions for output finite-time stability are given using Lyapunov functions. The theoretical results are supported by numerical examples