Abstract: This paper studies the stability of complex network systems with nonlinear coupled nodes. For the network coupying matries,the switching points of sub⁃systems discrete points in complex networks by using method that the Nimensinal complex network system transformed into the form of kronecker product.Then based on the Lyapunov function method, sufficient conditions for the stability of complex network systems are obtained. Based on the Lyapunov stability determination method, sufficient conditions for satisfying the stability of complex network systems are obtained. Finally, numerical examples are given to verify the effectiveness of the design method.

Key words: Coupling matrix, Complex network, Kronecker product, Lyapunov function

摘要： 研究了由非线性耦合节点组成的复杂网络系统的稳定性分析问题。针对系统中存在的网络耦合矩阵，基于系统子系统的切换点转化为离散点分析复杂网络系统稳定性的方法，并将N维的复杂网络系统转化为Kronecker积的形式进行计算，结合Lyapunov稳定性判定方法作为依据，得到满足复杂网络系统稳定性的充分条件。最后给出数值算例验证所设计方法的有效性。

关键词: 耦合矩阵, 　复杂网络, 　Kronecker积, 　Lyapunov函数