一般耦合结构时变时滞复杂网络的同步准则

研究一般耦合结构时变时滞复杂网络的同步问题,取消了复杂网络外部耦合矩阵是对称且不可简约的约束.对于一般的外部耦合矩阵,考虑了具有复数特征根的情况,并对复数域上的向量进行相应的处理.基于Lyapunov稳定性理论,利用矩阵分解技巧及线性矩阵不等式方法,通过构造适当的Lyapunov泛函,得到了网络系统实现同步的充分条件.为验证所得结论的有效性,对网络同步问题进行了数值仿真.仿真结果显示本文的同步准则较已有研究具有更小的保守性.

Synchronization criteria for general coupling complex networks with time varying delay

Synchronization problem for general coupling complex networks with time varying delay is studied. The restriction on the out-coupling matrix of a dynamical network that is always assumed to be symmetric or irreducible is removed. Complex eigenvalues for the general out-coupling matrix are considered and complex vectors are dealt with accordingly. Based on Lyapunov stability theory, the matrix decomposition technique and linear matrix inequalities(LMIs), the sufficient condition of synchronization stability is developed by constructing an appropriate Lyapunov function. In addition, synchronization problem of a numerical example is simulated to verify the effectiveness of the proposed conclusion. The results show that the condition is much less conservative than the existing ones in literature.