The combined functional approach to state estimation of delayed static neural network

Abstract

This dissertation investigates the H∞ state estimation for static neural networks with time-varying delays. In order to fully utilize delay information, a innovative Lyapunov–Krasovskii (L-K) functional is developed, which includes delay-product-type (DPT) terms both in the non-integral and single integral functionals, and the S-dependent integral term is introduced to combine with the single integral DPT functional for the first time. Then, in order to work effectively with the proposed L-K functional to lower the conservatism of the conclusion, generalized free-weighting-matrix integral inequality and other methods are selected. Furthermore, a more general gain inverse solution is given, and the gain matrix independent of the activation function is obtained, which removes the qualification that the activation function must be reversible. At last, numerical examples are used to explain the advantage of the proposed approach.