Synchronization Analysis for Nonlinear Complex Networks With Reaction-Diffusion Terms Using Fuzzy-Model-Based Approach

The synchronization of a class variable-coefficient complex networks with reaction-diffusion terms is investigated. The objective of this article is to synthesize a state-feedback controller, which is designed based on a Takagi-Sugeno (T-S) fuzzy model of the variable-coefficient complex network with reaction-diffusion terms such that the closed-loop system is synchronized. With the support of Green formula and some matrix inequality techniques, and utilizing the upper and lower bounds of the membership functions, membership-function-dependent (MFD) synchronization conditions guaranteeing the system's synchronization are obtained in the form of linear matrix inequalities (LMIs). A numerical example is presented to verify the analysis results and illustrate the effectiveness of the proposed synchronization conditions.