Delay-distribution-dependent synchronization of T-S fuzzy stochastic complex networks with mixed time delays

The paper investigates the synchronization problem for a class of Takagi-Sugeno(T-S) fuzzy stochastic complex dynamical networks with mixed time delays. The mixed time-delays are composed of discrete and distributed delays, the discrete time delays are assumed to be random and its probability distribution is known a prior. By employing the information of probability distribution of time delays, the original system is transformed into a T-S fuzzy model with stochastic parameter matrices. Based on the stochastic analysis techniques and the properties of the Kronecker product, delay-dependent synchronization criteria in the mean square are derived in the form of linear matrix inequalities which can be readily solved by using the LMI toolbox in Matlab, the solvability of derived conditions depends on not only the size of the delays, but also the probability of the delays taking values in some intervals. At last, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.