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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]