Finite-time robust stochastic synchronization of uncertain Markovian complex dynamical networks with mixed time-varying delays and reaction-diffusion terms via impulsive control

This study examines the problem of finite-time robust stochastic synchronization of uncertain Markovian complex dynamical networks with mixed time-varying delays and reaction-diffusion terms via impulsive control. Some novel and useful finite-time synchronization criteria are derived based on finite-time stability theory. This paper proposes a complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. By constructing a suitable Lyapunov-Krasovskii׳s (LK) functional and utilization of Jensen׳s inequality and Wirtinger׳s inequality, new synchronization criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.