A New Result on <i>H</i> <sub>∞</sub> State Estimation for Delayed Neural Networks Based on an Extended Reciprocally Convex Inequality
Jinxing Hu, Guoqiang Tan, Lei Liu
Abstract
This brief investigates the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state estimation problem for neural networks with time-varying delay. First, an extended reciprocally convex inequality based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> -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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> state estimation results are obtained to design suitable state estimator gains. Finally, simulation results are provided to verify the advantage of the presented method.