时变滞后随机大系统的稳定性：向量Lyapunov函数法

Stability of Time-Varying Large-Scale Delay Stochastic Systems: Vector Lyapunov Function Method

本文研究变系数、变时滞线性随机大系统的均方渐近稳定性．通过将Ｈａｌａｎａｙ不等式推广到高维空间、采用向量Ｌｙａｐｕｎｏｖ函数、运用Ｍ－矩阵等工具，得到了随机大系统的稳定性判据．文中模型考虑了子系统之间的交互随机干扰，所得稳定性判据是滞后无关的．

In this paper, mean-square asymptotic stability of large-scale stochastic systems with varying coefficients and varying delays is investigated, some stability criteria for large-scale stochastic systems are obtained via generalizing the Halanay inequality to high spaces, applying vector Lyapunov functions and employing M-matrices etc.. In the model of the paper,interconnected stochastic interferences among subsystems are considered. The stability criteria obtained are independent of delays.