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.