Delay-Dependent $H_{\infty }$ and Generalized $H_{2}$ Filtering for Delayed Neural Networks

This paper focuses on studying the H _infin and generalized H ₂ filtering problems for a class of delayed neural networks. The time-varying delay is only required to be continuous and bounded. Delay-dependent criteria are proposed such that the resulting filtering error system is globally exponentially stable with a guaranteed H _infin or generalized H ₂ performance. It is also shown that the designs of the desired filters are achieved by solving a set of linear matrix inequalities, which can be facilitated efficiently by resorting to standard numerical algorithms. It should be noted that, based on a novel bounding technique, several slack variables are introduced to reduce the conservatism of the derived conditions. Three examples with simulation results are provided to illustrate the effectiveness and performance of the developed approaches.