Mean square H∞ synchronization of coupled stochastic partial differential systems

In this paper, the criterion and control are considered for the mean square H∞ synchronization of coupled stochastic partial differential systems (SPDSs). Based on the integral Lyapunov-like functional and by virtue of completing squares technique, a sufficient criterion is provided to guarantee the mean square H∞ synchronization. The effect of spatial domain on the mean square H∞ synchronization is also embodied in this criterion. When the coupled SPDSs cannot achieve the mean square H∞ synchronization, the adaptive controllers are adopted for the coupled SPDSs, and the effectiveness of the adaptive controllers is verified via a rigorous mathematical analysis. When the number of the nodes in the complex networks is large, pinning control is a natural choice. The adaptive pinning control strategy is also presented and a criterion is obtained which guarantees the mean square H∞ synchronization of coupled SPDSs. Numerical experiments are also given to illustrate the correctness of our results.