In this paper, the robust filtering problem for uncertain complex networks with time-varying state delay and stochastic nonlinear coupling based on $H_{\infty }$ performance criterion is studied. The random connections of coupling nodes are represented by utilizing independent random variables and the multiple fading measurements phenomenon is characterized by introducing diagonal matrices with independent stochastic elements. Moreover, the probabilistic time-varying delays in the measurement outputs are described by white sequences with the Bernoulli distributions. Furthermore, All system’s matrices are supposed to have uncertainty and a quadratic bound is assumed for nonlinear part of the network. This bound can be obtained by solving a sum of squares (SOS) optimization problem. By applying the Lyapunov theory, we design a robust filter for each node of the network so that the filtering error system is asymptomatically stable and the $H_{\infty }$ performances are met. Then, the parameters of the filters are achieved by solving a linear matrix inequality (LMI) feasibility problem. Finally, the applicability and performance of the proposed $H_{\infty }$ filtering approach are demonstrated via a practical example.

本文研究了具有时变状态延迟和随机非线性耦合的不确定复杂网络的鲁棒滤波问题$H_{\infty }$性能标准进行了研究。耦合节点的随机连接用独立随机变量表示，多重衰落测量现象通过引入具有独立随机元素的对角矩阵来表征。此外，测量输出中的概率时变延迟由具有伯努利分布的白色序列描述。此外，所有系统的矩阵都应该具有不确定性，并且对于网络的非线性部分假设二次界。这个界限可以通过求解平方和 (SOS) 优化问题来获得。通过应用李雅普诺夫理论，我们为网络的每个节点设计了一个鲁棒的滤波器，使得滤波误差系统是无症状稳定的，并且$H_{\infty }$表演得到满足。然后，通过求解线性矩阵不等式 (LMI) 可行性问题来获得滤波器的参数。最后，提出的适用性和性能$H_{\infty }$通过一个实际示例演示了过滤方法。