In this paper, we estimate the domain of attraction of the origin of two interconnected nonlinear systems. For each subsystem we introduce an auxiliary system and assume that the origin is locally robustly asymptotically stable. Then an integral input-to state stable Lyapunov function for each subsystem on a bounded set is constructed via Zubov’s method and the introduced auxiliary system. A local version of small gain theorem is proposed. It is easier to check if the conditions of the proposed small gain theorem are satisfied. Moreover, an estimate for the domain of attraction for the whole system is obtained based on the proposed small gain theorem and the computed integral input-to state stable Lyapunov functions. We illustrate the effectiveness of the main results by an academic example.

在本文中，我们估计了两个相互连接的非线性系统起源的吸引域。对于每个子系统，我们引入一个辅助系统，并假设原点在局部鲁棒渐近稳定。然后，通过Zubov方法和引入的辅助系统，为有界集合上的每个子系统构建了一个完整的输入到状态稳定Lyapunov函数。提出了局部形式的小增益定理。更容易检查所提出的小增益定理的条件是否得到满足。此外，基于提出的小增益定理和计算出的积分输入到状态稳定的Lyapunov函数，获得了整个系统的吸引域的估计。我们通过一个学术实例来说明主要结果的有效性。