Delay-dependent synchronization of T-S fuzzy Markovian jump complex dynamical networks

Abstract In this paper, a delay-dependent synchronization criteria for Markovian jump complex dynamical networks subject to time-varying coupling delays and external disturbances are proposed via Takagi-Sugeno (T-S) fuzzy approach. The class of Markovian jump complex dynamical networks is described by a fuzzy model composed of two levels such as a crisp level which represents the jumps and a fuzzy level which describes the system nonlinearities. An asymptotic synchronization criterion is obtained by employing fuzzy controller with the mixed H ∞ and passivity performance index ν > 0 . Further, by constructing a novel Lyapunov-Krasovskii functional along with the extended integral inequality and using the properties of Kronecker product and convex combination approach, a set of sufficient constraints is derived in the form of linear matrix inequalities and checked for its feasibility using MATLAB software. At last, numerical simulations including the Lorentz system are given to demonstrate the applicability and effectiveness of the developed results.