On the Uniform Finite-Time Stability of Continuous Linear Time-Varying Systems: A Numerical Algorithm

The paper deals with the uniform finite-time stability (UFTS) of continuous linear time-varying (LTV) systems. Firstly, a necessary and sufficient condition for the UFTS of continuous LTV systems is devised with the idea of computing the envelope of all the trajectories of the considered system. Then, a corollary is obtained under the perspective of numerical computation. Further, based on the obtained corollary, a novel numerical algorithm is designed by utilizing the Lipschitz continuity of certain functions. With the proposed algorithm, only limited numerical computation is needed when analyzing the UFTS of continuous LTV systems. Compared with the existing Lyapunov-like function method, one needn't constructing Lyapunov-like functions. Moreover, the obtained corollary just requires being checked at a limited number of time points. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the proposed results.