In this paper, the reliable exponential ${\mathcal{H}}_{\infty }$ filtering issue is studied for switched reaction-diffusion neural networks subject to exterior interference. The purpose is to design a Luenberger observer to make sure that the filtering error system possesses a pre-defined exponential ${\mathcal{H}}_{\infty }$ interference-rejection level against possible sensor failures. An analysis result on the exponential ${\mathcal{H}}_{\infty }$ performance is presented by the use of a Lyapunov functional together with a few inequalities. On its basis, a linear matrix inequalities-based design scheme for the Luenberger observer is proposed by getting rid of the nonlinear terms composed of the Lyapunov matrix, the gain matrix, and an uncertainty matrix caused by the sensor failures. In the case when the factors of sensor failures and reaction-diffusion are not concerned, the design scheme is shown to be an improvement over an existing design scheme. Finally, two examples are given to demonstrate the applicability and reduced conservatism of the obtained results, respectively.

在本文中，可靠的指数 ${\mathcal{H}}_{\infty }$研究了受外部干扰的切换反应扩散神经网络的滤波问题。目的是设计一个 Luenberger 观测器，以确保滤波误差系统具有预定义的指数${\mathcal{H}}_{\infty }$针对可能的传感器故障的干扰抑制水平。指数分析结果${\mathcal{H}}_{\infty }$性能是通过使用李雅普诺夫泛函和一些不等式来呈现的。在此基础上，去除了由Lyapunov矩阵、增益矩阵和传感器故障引起的不确定矩阵组成的非线性项，提出了一种基于线性矩阵不等式的Luenberger观测器设计方案。在不考虑传感器故障和反应扩散因素的情况下，该设计方案被证明是对现有设计方案的改进。最后，给出两个例子，分别说明所得结果的适用性和降低的保守性。