State Estimation for Static Neural Networks With Time-Varying Delays Based on an Improved Reciprocally Convex Inequality

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.