Synchronization of Fractional Reaction-Diffusion Complex Networks With Unknown Couplings
Mouquan Shen, Chen Wang, Qing‐Guo Wang, Yonghui Sun, Guangdeng Zong
Abstract
This paper delves into the synchronization of factional uncertain reaction-diffusion complex network. An adaptive scheme composed of time <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$t$</tex-math></inline-formula> and space <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$x$</tex-math></inline-formula> 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.