The distributed \(H_\infty \) state estimation of delayed sensor network is dealt with in this paper. To deeply reflect the time-delay phenomenon in the process of information fusion, a model containing state time-varying delay and different communication delays is set up. Afterwards, a fresh Lyapunov–Krasovskii functional (LKF) is given, which contains different kinds of time delays, delay-dependent matrix and multiple integral terms. Meanwhile, in order to cooperate with the constructed LKF to bring down the conservatism of the result effectively, relaxed-function-based single integral inequality and convex combination are employed to estimate the functional derivative. Thus, a less conservative criterion is gained to guarantee the asymptotic stability with desirable attenuation level of the estimation error system. Several simulation examples are used to testify the validity of the proposed approach.

分布式\（H_ \ infty \）本文讨论了延迟传感器网络的状态估计问题。为了深入反映信息融合过程中的时延现象，建立了一个包含状态时变时延和不同通信时延的模型。然后，给出了一个新的Lyapunov–Krasovskii函数（LKF），其中包含不同类型的时间延迟，依赖于延迟的矩阵和多个积分项。同时，为了与构造的LKF有效地降低结果的保守性，采用基于松弛函数的单个积分不等式和凸组合来估计函数导数。因此，获得了较不保守的标准，以保证渐进稳定性，并具有估计误差系统的期望衰减水平。