Passivity-based synchronization of stochastic switched complex dynamical networks with additive time-varying delays via impulsive control

The issue of passivity-based synchronization for switched complex dynamical networks with additive time-varying delays, stochastic and reaction-diffusion effects is investigated. In this paper, stochastic, passivity theory and impulsive control are taken to investigate this problem. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Ito differential rule and matrix analysis techniques, we established a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the switched complex dynamical networks is robustly passive in the sense of expectation. By constructing a suitable Lyapunov-Krasovskii functional using Jensen's inequality, integral inequality technique and the passivity criterion of addressed complex dynamical networks is obtained. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares. Illustrative example is presented to demonstrate the effectiveness and usefulness of the proposed results.