Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays

This paper deals with the synchronisation problem for an array of coupled complex discrete-time networks with the presence of randomly occurring information. The time-varying delays, parameter uncertainties and nonlinearities enter into the system in a random way and such randomly occurring time-delays, randomly occurring uncertainties and randomly occurring sector-like nonlinearities obey certain mutually uncorrelated Bernoulli-distributed white-noise sequences. By employing direct delay decomposition approach and constructing suitable Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the synchronisation criteria for the complex networks with randomly occurring information in terms of linear matrix inequalities. Finally, in numerical examples, synchronisation of Barabasi Albert scale-free networks and chaotic synchronisation of Lorenz system are rendered to exemplify the effectiveness and applicability of the proposed results.