Aperiodically Intermittent Fixed-Time Synchronization of Coupled Reaction-Diffusion Systems via Average Control Rate

In this study, the fixed-time synchronization (FTSn) problem is investigated for coupled reaction-diffusion systems (RDSs) with time-varying delay based on an aperiodically intermittent control (AIC) strategy. For the fixed-time control, the convergence time can be estimated in advance, irrespective of initial states. Additionally, unlike the previous studies with the semi-intermittent control strategy, the FTSn is achieved for the coupled RDSs via completely AIC by adopting the average control rate, then the mechanism is more general. Meanwhile, the utilization of average control rate indicates that the results obtained are less conservative. Furthermore, a new auxiliary function is designed to demonstrate that the fixed-time convergence of the coupled RDSs can be guaranteed with or without the presence of time-varying delay. Finally, numerical examples are provided to verify the effectiveness of the theoretical results.