Synchronization for Semi-Markovian Jumping Reaction-Diffusion Complex Dynamical Networks: A Space-Time Sampled-Data Control Scheme

This paper focuses on synchronization for Complex Dynamic Networks (CDNs) subject to semi-Markovian jumping topologies. Two different models (PDE- and ODE-based models) are proposed and investigated separately. First, to avoid large control costs, a space-time sampled-data controller is introduced for the system under consideration to conserve more communication resources than a normal time sampled-data controller. Second, a two-sided looped-functional that is superior to the traditional ones is constructed to capture more state information in a sampling interval. Further, to reduce the conservatism of the results, the Bessel–Legendre inequality is used, and several sufficient synchronization conditions are established for different CDN models with less conservatism. Finally, examples of some applications and comparative studies are provided to illustrate the effectiveness and superiority of the theoretical results.