Abstract: A discrete-time complex dynamical network model is achieved in view of the phenomenon of data missing and channel disturbance during the information transmission among the nodes and by using data missing characterized with Bernoulli stochastic sequence. A novel [H∞]control scheme is proposed for the above model based on Lyapunov stability theory combining with stochastic analysis such that the controlled outputs of complex dynamical network satisfy an [H∞] performance index. An [H∞]control criterion is established for discrete-time complex dynamical networks with data missing in the form of linear matrix inequalities. A numerical simulation is carried out by using a discrete-time complex dynamical network with 20 nodes. The simulation results demonstrate the effectiveness and validity of the proposed [H∞] controller for a discrete-time complex dynamical network.

Key words: complex dynamical networks, data missing, stochastic analysis, [H∞]control, linear matrix inequality

摘要： 考虑到复杂动态网络节点之间的信息传输存在数据丢失和信道干扰的现象，利用Bernoulli随机序列描述数据丢失，得到离散复杂动态网络模型。在此模型基础上，基于Lyapunov稳定性理论和随机分析方法，提出了一种新的[H∞]控制方案，使得复杂动态网络的控制输出满足一定的[H∞]性能指标。该控制方案以线性矩阵不等式形式描述，给出了存在数据丢失时，离散复杂动态网络的[H∞]控制器设计准则。以20个节点的离散复杂动态网络为例，进行了数值仿真。仿真结果表明所设计的[H∞]控制器能够使耦合数据丢失的复杂动态网络均方渐近稳定，且满足一定的[H∞]性能指标。

关键词: 复杂动态网络, 数据丢失, 随机分析, [H&infin, ]控制, 线性矩阵不等式