Finite-Time Stability of Continuous Autonomous Systems

Abstract. Finite-time stability is dened for equilibria of continuous but non-Lipschitzian autonomous systems. Continuity, Lipschitz continuity, and Hölder continuity of the settling-time function are studied and illustrated with several examples. Lyapunov and converse Lyapunov re-sults involving scalar dierential inequalities are given for nite-time stability. It is shown that the regularity properties of the Lyapunov function and those of the settling-time function are related. Consequently, converse Lyapunov results can only assure the existence of continuous Lyapunov func-tions. Finally, the sensitivity of nite-time-stable systems to perturbations is investigated.