A New Result on H∞ State Estimation for Delayed Neural Networks Based on an Extended Reciprocally Convex Inequality

This brief investigates the
$H_{\infty }$
state estimation problem for neural networks with time-varying delay. First, an extended reciprocally convex inequality based on
$r$
-degree polynomial matrix inequality is presented, which considers more information of high-order of the time delay and more flexibility can be obtained. Second, the extended reciprocally convex inequality and some integral inequalities are used to derive a tight upper bound of the Lyapunov-Krasovkii functional derivative. As a result, some less conservative
$H_{\infty }$
state estimation results are obtained to design suitable state estimator gains. Finally, simulation results are provided to verify the advantage of the presented method.