Exponential synchronization of stochastic complex dynamical networks with impulsive perturbations and Markovian switching

This paper investigates the exponential synchronization problem of stochastic complex dynamical networks with impulsive perturbations and Markovian switching. The complex dynamical networks consists of κ modes and the networks switch from one mode to another according to a Markovian chain with known transition probability. Basing on the Lyapunov functional method and stochastic analysis, by employing M-matrix approach, some sufficiency conditions are presented to ensure the exponential synchronization of stochastic complex dynamical networks with impulsive perturbations and Markovian switching, and the upper bound of impulsive gain is evaluated. At the end of this paper, a numerical examples are included to show the effectiveness of our results.