Neuronal state estimation of neural networks is a fundamental issue, aiming at estimating neuronal states from contaminated neural measurement outputs. Inspired by extensive applications of neural networks, neuronal state estimation has become a hot research topic in the last decade. This paper presents an overview of neuronal state estimation of neural networks with time-varying delays. First, two kinds of state estimators are analyzed, and their differences are uncovered. Second, recent developments of a Lyapunov–Krasovskii functional method for performance analysis of estimation error systems are surveyed deeply, and some existing methods to design suitable state estimators are summarized with insightful understanding. Third, brief analysis of event-triggered neuronal state estimations of delayed neural networks is made. Finally, some challenging issues that need to be addressed in the near future are listed and briefly discussed.
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