An improved sampled-data synchronization criterion for delayed neural networks with two-type transmission delays

This paper investigates the sampled-data synchronization problem for delayed neural networks (DNNs) with two-type transmission delays by input delay approach. We propose novel Lyapunov functionals consisting of continuous Lyapunov functionals and looped-functionals by exploiting the transmission delays induced by neurons and the communication network and the input delay induced by the sampler. The proposed Lyapunov functionals utilize the transmission delays and a mixed delay of the network transmission delay and the input delay into the augmented vector and the integral functionals. The proposed looped-functionals utilize an additional interval [t−ηk,tk−τt] which is zero at t=tk+1 into the integral functionals and include an additional function by exploiting the state vectors related to sampling pattern. Furthermore, this paper proposes a zero equality with a slack variable for the elements of the augmented vector and relaxes the positive conditions of some matrices in the proposed Lyapunov functionals. From the proposed Lyapunov functionals and the relaxations, we derive the stabilization criteria represented as linear matrix inequalities. The simulation result presents the superiority and validity of the proposed criteria.