Sampled-data synchronization of randomly coupled reaction–diffusion neural networks with Markovian jumping and mixed delays using multiple integral approach

This paper is devoted to investigate the problem of global asymptotic synchronization of an array of N randomly coupled reaction–diffusion neural networks with Markovian jumping parameters and mixed delays using sampled-data control technique. The jump parameters are determined by a continuous-time, discrete-state Markovian chain, and the mixed time delays under consideration comprise both discrete and distributed delays. A multiple integral inequality is proposed firstly in Markovian jump reaction–diffusion neural networks with mixed delays. Through constructing appropriate Lyapunov–Krasovskii functional including multiple integral terms, some novel synchronization criteria in terms of linear matrix inequalities are derived. The obtained LMIs can be easily verified for feasibility through any of the available softwares. Finally, numerical examples with simulations are provided to illustrate the effectiveness of the proposed theoretical results.