Finite-time synchronization of intermittently controlled reaction–diffusion systems with delays: A weighted LKF method

Abstract

Considering the fact that existing methodologies for finite-time control are difficult to simultaneously overcome the difficulties induced by the effects of reaction–diffusion and time delay when intermittent control is confronted, this paper explores a novel Lyapunov–Krasovskii functional (LKF) method to investigate the finite-time synchronization of delayed reaction–diffusion systems. By designing a simple intermittent control and a weighted LKF, a general finite-time stability criterion is established first. Then, sufficient conditions for the finite-time synchronization of the interested system are given, where the weight factor of the LKF has a heavy influence on the settling time. Several important corollaries are also given to specify the usefulness and generality of the weighted LKF method and the finite-time stability criterion. Finally, a numerical example is provided to verify the new findings, and an image encryption algorithm is presented to validate the useful application of theoretical results.