New Sufficient Conditions for Finite Time Stability of Nonlinear Time Delay Systems

In this note, we propose two new sufficient conditions on finite time stability for nonlinear time delay systems. First, a sufficient condition is proposed to verify the stability of systems by employing a continuously differentiable Lyapunov-Krasovskii functional with indefinite derivative. Second, another sufficient condition is proposed by extending the Razumikhin approach, moreover, the corresponding estimate on convergence time of systems is also given. The results obtained herein are less conservative than the existing methods, i.e., they relax the restriction that the Lyapunov function of systems has to be decreasing in the convergence process. Finally, two numerical examples are provided to show the effectiveness of the theoretical results.