线性时变系统有限时间稳定性的数值判定算法

Numerical algorithm for analyzing the finite-time stability of linear time-varying systems

针对系统的初值和系统的状态均限定在多面体集合的情形,本文从数值计算角度研究了连续线性时变(linear time-varying, LTV)系统有限时间稳定性(finite-time stability, FTS)的判定问题.首先,通过求解特定的函数优化问题,给出了该类系统有限时间稳定的充分必要条件.然后,利用所得充分必要条件以及特定函数的Lipschitz连续性质,从数值计算角度给出了判定该类系统有限时间稳定性的充分条件.进一步,基于所得充分条件,将特定的函数优化问题转化为相应的线性规划,提出了一种判定该类系统有限时间稳定性的数值算法.最后,给出的4个数值算例说明了本文算法的正确性和有效性,以及相比已有结果的优越性.

Under the perspective of numerical computation, the paper investigates the finite-time stability (FTS) analysis of continuous linear time-varying (LTV) system when its initial values and its states are all confined within polyhedral sets. 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 obtained condition and the Lipschitz continuity of a certain function, the paper gives two sufficient conditions for deciding the FTS of continuous LTV systems under the perspective of numerical computation. Further, based on the obtained sufficient conditions, a numerical algorithm for analyzing the FTS of continuous LTV systems is detailedly designed by converting a certain function optimization problem into a corresponding linear programming. Finally, four numerical examples are given to illustrate the correctness and effectiveness of the proposed algorithm. Moreover, the advantages of the proposed algorithm over the existing methods are also verified by the numerical examples.