Synchronization of Coupled Markovian Reaction–Diffusion Neural Networks With Proportional Delays Via Quantized Control

Abstract

The asymptotic synchronization of coupled reaction-diffusion neural networks with proportional delay and Markovian switching topologies is considered in this brief where the diffusion space does not need to contain the origin. The main objectives of this brief are to save communication resources and to reduce the conservativeness of the obtained synchronization criteria, which are carried out from the following two aspects: 1) mode-dependent quantized control technique is designed to reduce control cost and save communication channels and 2) Wirtinger inequality is utilized to deal with the reaction-diffusion terms in a matrix form and reciprocally convex technique combined with new Lyapunov-Krasovskii functional is used to derive delay-dependent synchronization criteria. The obtained results are general and formulated by linear matrix inequalities. Moreover, combined with an optimal algorithm, control gains with the least magnitude are designed.