Synchronization of TS fuzzy complex dynamical networks with time-varying impulsive delays and stochastic effects

In this paper, global exponential synchronization of Takagi–Sugeno (TS) fuzzy complex dynamical networks with multiple time-varying delays and stochastic perturbations is studied via delayed impulsive distributed control. Both impulsive and continuous parts of the fuzzy model have different multiple time-varying delays, which make the considered model general and practical. A novel lemma on exponential stability of impulsive delayed differential equations was established, in which the impulsive functions exhibit multiple time-varying delays. By utilizing the proposed lemma, Lyapunov functions, the stochastic analysis techniques, and the Kronecker product, general criteria ensuring global exponential synchronization in mean square of the addressed TS fuzzy complex networks are obtained. Moreover, the theory of function minimum value is utilized to reduce the conservativeness of the obtained synchronization criteria, which also makes them simple and easy to be verified in practical applications. Results of this paper improve and extend some existing ones. Numerical simulations including small-world network coupled with time-delayed Lorenz system are given to show the effectiveness of the theoretical results.