Abstract: The guaranteed cost synchronization control problem of some general complex dynamical networks with time-varying delay is investigated. A dynamic feedback controller is designed for the system guaranteed cost synchronization. Meanwhile, due to many nodes in the complex networks and the complex of the direct control, it is also investigated that using the pinning control to make the system achieve guaranteed cost synchronization. Based on the Lyapunov stability theory and the matrix inequality, the sufficient conditions are obtained for the existence of the guaranteed cost controller with time-varying delay in complex network. In the condition of the asymptotic stability  of the system, the dynamic feedback controller is designed for making the performance index of the system meet certain requirements. Finally, the feasibility of the proposed method is demonstrated by numerical examples.

Key words: complex network, synchronization, pining control, guaranteed cost control, time-varying delay

摘要： 针对具有可变时滞的复杂网络系统，研究此类系统的同步保性能控制问题。为了使系统同步保性能，设计了一种动态反馈控制器；同时，由于复杂网络的节点较多，考虑到直接控制比较复杂，所以又研究了利用牵制控制使系统达到同步保性能控制的方法。主要运用Lyapunov稳定性理论并结合矩阵不等式处理方法，得出了具有可变时滞性复杂网络系统同步保性能控制器存在的充分条件。所设计的动态反馈控制器在保证系统的渐近稳定条件下使系统的性能指标满足一定的要求。最后给出两个数值仿真说明其有效性。

关键词: 复杂网络, 同步, 牵制控制, 保性能, 可变时滞