Synchronization of Fractional Reaction-Diffusion Complex Networks With Unknown Couplings

This paper delves into the synchronization of factional uncertain reaction-diffusion complex network. An adaptive scheme composed of time $t$ and space $x$ is utilized to handle unknown couplings. An output-strict passivity lemma is established by means of Green theorem, Kronecker product and the Lyapunov stability theorem. Different from classical synchronous approaches by constructing controllers, a criterion in terms of linear matrix inequality is built on the passivity lemma, Laplace transform and inverse transform to make the resultant closed-loop system be synchronization. Two examples are provided to validate the validity of the proposed methods.