一类线性互联大系统的关联稳定性判定

Connective stability criterion of a class of linear interconnected large-scale systems

动态图可以描述互联大系统的拓扑结构。动态图的增广矩阵包含了动态图的所有结构信息。引入动态图增广矩阵的相关理论,结合M-矩阵理论知识,提出了一类线性互联大系统的关联稳定性的判定方法。利用Lyapunov函数及Lyapunov梯度函数,推导出一个判定矩阵H,通过判定矩阵H是否对角占优和是否为M-矩阵,判定线性互联大系统的关联稳定性。算例表明,判定矩阵的参数计算简单,容易获取,有利于判定线性互联大系统的关联稳定性。

From the view of graph theory, dynamic graph can describe the topological structure of interconnected system, and the augmented matrix of dynamic graph contains all the structural information of dynamic graph. Therefore, the augmented matrix of dynamic graph is introduced by combining with the M-matrix theory, the connective stability criterion of a class of linear interconnected large scale systems is proposed by Lyapunov function and Lyapunov-gradient function. A judgment matrix is derived, through the judgment matrix is diagonally dominant and whether the M-matrix is, the connective stability of linear interconnected large-scale systems is judged. The results show that calculation of judging matrix calculation is simple, easy to obtain and is useful to judge connective stability of linear interconnected large-scale systems.