New Results on State Estimation of Static Neural Networks with Time-Varying Delays

Abstract

This paper focuses on studying the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance state estimation problem for static neural networks (SNNs) with time-varying delays. Consider the estimation problem for delayed SNNs, the previously well-known Lyapunov-Krasovski functional (LKF) methods are devoted to constructing more and more complex functionals, in which each term is positive definite function. Hence it is difficult to solve and optimize in designing estimators. In this paper, the simple delay product type LKF with negative definite terms is established for the use of the Wirtinger based inequality together with mixed convex combination approach. The delay dependent conditions in terms of linear matrix inequalities (LMIs) are obtained which lead to less conservative and more flexible estimator design results. Finally, a numerical example is given to demonstrate the merits over the existing ones.