Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data

Abstract

In this paper, the problem of synchronization via sampled-data control is considered for stochastic delayed neural networks with Lévy noise and Markovian switching. The purpose of the problem addressed is to derive a sufficient condition and a sampled-data control law such that the dynamics of the error system is stable in mean square, and thus the synchronization can be achieved for the master system and the slave system. By generalized Itô’s formula and the construction of Lyapunov functional, an LMI-based sufficient condition is established to ensure the synchronization of the two systems. The control law is determined simultaneously, which depends on the switching mode, time delay, and the upper bound of sampling intervals. A numerical example is provided to verify the usefulness of the proposed criterion.