Mixed H∞/ $H_{\infty }/$passive exponential function projective synchronization of delayed neural networks with hybrid coupling based on pinning sampled-data control

Abstract This paper presents the problem of mixed H∞ $H_{\infty }$/passive exponential function projective synchronization of delayed neural networks with constant discrete and distributed delay couplings under pinning sampled-data control scheme. The aim of this work is to focus on designing of pinning sampled-data controller with an explicit expression by which the stable synchronization error system is achieved and a mixed H∞ $H_{\infty }$/passive performance level is also reached. Particularly, the control method is designed to determine a set of pinned nodes with fixed coupling matrices and strength values, and to select randomly pinning nodes. To handle the Lyapunov functional, we apply some new techniques and then derive some sufficient conditions for the desired controller existence. Furthermore, numerical examples are given to illustrate the effectiveness of the proposed theoretical results.