Local synchronization for non-linear stochastic functional systems under sampling control

Abstract

This paper presents a local exponential driving-response synchronization framework for stochastic non-linear functional systems (NLSFSs) under the sampling control. In contrast to previous studies of local synchronization of deterministic functional systems, we extend this to local synchronization of stochastic functional systems. For the sampling control, we define a partition of sampling instants. Combined with Halanay inequality and stochastic analysis technique, we also prove that under some sufficient conditions, including the maximum sampling interval, i.e. the upper bound of the partition, the NLSFSs can be locally synchronized under the sampling control with the partition. Our results show that the synchronization is dependent on the time delay, stochastic disturbance, and the maximum sampling interval. Then the results are applied to a class of circuit systems, and some synchronization criteria for the systems are provided. Finally, a numerical example is showcased and the simulation results illustrate the effectiveness of our theoretical results.