\(H_{\infty }\) state estimation is addressed for continuous-time neural networks in the paper. The norm-bounded uncertainties are considered in communication neural networks. For the considered neural networks with uncertainties, a reduced-order \(H_{\infty }\) state estimator is designed, which makes that the error dynamics is exponentially stable and has weighted \(H_{\infty }\) performance index by Lyapunov function method. Moreover, it is also given the devised method of the reduced-order \(H_{\infty }\) state estimator. Then, considering that sampling the output y(t) of the neural network at every moment will result in waste of excess resources, the event-triggered sampling strategy is used to solve the oversampling problem. In addition, a devised method is also given for the event-triggered reduced-order \(H_{\infty }\) state estimator. Finally, by the well-known Tunnel Diode Circuit example, it shows that a lower order state estimator can be designed under the premise of maintaining the same weighted \(H_{\infty }\) performance index, and using the event-triggered sampling method can reduce the computational and time costs and save communication resources.
