New H_∞ state estimation criteria of delayed static neural networks via the Lyapunov–Krasovskii functional with negative definite terms

In the estimation problem for delayed static neural networks (SNNs), constructing a proper Lyapunov–Krasovskii functional (LKF) is crucial for deriving less conservative estimation criteria. In this paper, a delay-product-type LKF with negative definite terms is proposed. Based on the third-order Bessel–Legendre (B–L) integral inequality and mixed convex combination approaches, a less conservative estimator design criterion is derived. Furthermore, the desired estimator gain matrices and the H_∞ performance index are obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.