Bounded H∞ synchronization for time‐varying networks with probability‐dependent information

This paper addresses the bounded H_∞ synchronization problem for the time‐varying coupled networks with stochastic noises and randomly occurring nonlinearities over a finite horizon. The bounded H_∞ synchronization performance constraint is proposed to quantify the degree of the synchronization regarding the exogenous disturbances. The nonlinearities considered in this paper are assumed to satisfy the sector‐like conditions and characterized by a time‐varying Bernoulli distribution with measurable probability in real time. Based on the Kronecker product and the Hadamard product, a sufficient condition is established firstly to ensure the bounded H_∞ synchronization of the network by utilizing the probability‐dependent method. Then the obtained criterion is further converted into a computationally available one by transforming the time‐varying probability into a polytopic form, which is presented in terms of matrix inequalities and hence can be verified easily by applying the Matlab toolbox. Finally, simulation examples are given to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.