An Asymmetric Lyapunov Functional Approach for Outlier‐Resistant Remote Resilient State Estimation of Semi‐Markov Switching Reaction‐Diffusion Neural Networks

ABSTRACT This article marks the pioneering effort to explore the remote state estimation (RSE) issue for reaction‐diffusion neural networks (RDNNs) involving semi‐Markov switching coefficients. In the first place, to effectively capture the complex spatial‐temporal dynamics inherent in neural networks (NNs), a semi‐Markov switching NN model incorporating reaction‐diffusion phenomenon is formulated. Subsequently, to acquire the accurate state information of the semi‐Markov switching RDNNs in the context of a remote communication environment, an outlier‐resistant resilient state estimator (ORSE) is developed, accounting for probabilistic gain fluctuations in the estimator and the presence of measurement outliers. This design aims to enhance the robustness of the remote state estimator. Additionally, a novel asymmetric Lyapunov‐Krasovskii functional (LKF) is constructed to alleviate the positive definiteness constraint and reduce conservatism. Furthermore, by employing the LKF approach, sufficient conditions of the asymptotic stability with prescribed performance for the error system are derived. Ultimately, the feasibility of the proposed method is validated through two numerical simulation examples.