Abstract: Based on the result of exponential stability of a class of large-scale systems with variable delays，this paper presents an estimating strategy on the exponential convergence rate of the class of large-scale systems．By this estimating method，the exponential convergence rate is estimated，and the estimating inequality of the exponential convergence rate of the class of large-scale systems with variable delays is obtained．The estimating strategy is based on the properties of M-matrix and the test matrix which is constructed by employing the coeficient matrices of the large-scale systems and the solutions of the Lyapunov equations interconnected with the large-scale systems． Since the method is independent of the delays and simplifies the calculation，it is easy to apply in practice．

Key words: global exponential stability, M-matrix, exponential convergence rate large-scale systems, time delays

摘要： 基于一类变时滞大系统全局指数稳定性的研究结果，提出了一种大系统指数收敛率的估计方法．利用此方法对该系统的指数收敛率进行了估计，得到了系统指数收敛率的估计式．该方法以大系统的系数矩阵以及与大系统关联的李雅普诺夫矩阵方程的解构造判定矩阵。利用M一矩阵理论，来确定系统的指数收敛率，计算简便，且与时间滞后量无关，便于在实践中应用．

关键词: 全局指数稳定性, M矩阵, 指数收敛率, 大系统, 时间滞后