Finite-time Stability Analysis of Linear Time-varying Systems: A Numerical Algorithm

Under the perspective of numerical computation, this paper investigates the finite-time stability (FTS) of continuous linear time-varying (LTV) systems when all its initial values are confined within a given polyhedral set while all its states are confined within a given ellipsoidal set. First, by solving a certain function optimization problem, the paper proposes a necessary and sufficient condition to guarantee the FTS of continuous LTV systems. Then, by utilizing the Lipschitz continuity of a certain function, two sufficient conditions to verify the FTS and finite-time instability of continuous LTV systems are proposed under the perspective of numerical computation, respectively. Furthermore, a novel numerical algorithm for analyzing the FTS of continuous LTV systems is deigned by converting a certain function optimization problem into a corresponding quadratic programming. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.