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Abstract 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. [ABSTRACT FROM AUTHOR]

This paper is concerned with global asymptotic stability of a neural network with a time-varying delay, where the delay function is differentiable uniformly bounded with delay-derivative bounded from above. First, a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions. This inequality provides a tighter bound in the form of a convex combination than some existing ones. Second, by constructing proper Lyapunov–Krasovskii functional, global asymptotic stability of the neural network is analyzed for two types of the time-varying delays depending on whether or not the lower bound of the delay derivative is known. Third, noticing that sufficient conditions on stability from estimation on the derivative of some Lyapunov–Krasovskii functional are affine both on the delay function and its derivative, allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study. Finally, two numerical examples are given to substantiate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This brief is concerned with global asymptotic stability of a neural network with a time-varying delay. First, by introducing an auxiliary vector with some nonorthogonal polynomials, a slack-matrix-based integral inequality is established, which includes some existing one as its special case. Second, a novel Lyapunov–Krasovskii functional is constructed to suit for the use of the obtained integral inequality. As a result, a less conservative stability criterion is derived, whose effectiveness is finally demonstrated through two well-used numerical examples. [ABSTRACT FROM AUTHOR]

This brief is concerned with the problem of neural state estimation for static neural networks with time-varying delays. Notice that a Luenberger estimator can produce an estimation error irrespective of the neuron state trajectory. This brief provides a method for designing such an estimator for static neural networks with time-varying delays. First, in-depth analysis on a well-used reciprocally convex approach is made, leading to an improved reciprocally convex inequality. Second, the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time-derivative of some Lyapunov–Krasovskii functional. As a result, a novel bounded real lemma (BRL) for the resultant error system is derived. Third, the BRL is applied to present a method for designing suitable Luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters. Finally, it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones. [ABSTRACT FROM PUBLISHER]

This paper is concerned with event-triggered generalized dissipativity filtering for a neural network (NN) with a time-varying delay. The signal transmission from the NN to its filter is completed through a communication channel. It is assumed that the network measurement of the NN is sampled periodically. An event-triggered communication scheme is introduced to design a suitable filter such that precious communication resources can be saved significantly while certain filtering performance can be ensured. On the one hand, the event-triggered communication scheme is devised to select only those sampled signals violating a certain threshold to be transmitted, which directly leads to saving of precious communication resources. On the other hand, the filtering error system is modeled as a time-delay system closely dependent on the parameters of the event-triggered scheme. Based on this model, a suitable filter is designed such that certain filtering performance can be ensured, provided that a set of linear matrix inequalities are satisfied. Furthermore, since a generalized dissipativity performance index is introduced, several kinds of event-triggered filtering issues, such as $H_\infty $ filtering, passive filtering, mixed H_\infty $ and passive filtering, (Q,S,R)$ -dissipative filtering, and – \mathcal L_{\infty } filtering, are solved in a unified framework. Finally, two examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]