PID Control for Output Synchronization of Multiple Output Coupled Complex Networks

Linhao Zhao, Shiping Wen, Min Xu, Kaibo Shi, Song Zhu, Tingwen Huang

Abstract: This article attempts to address output synchronization and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization problems for multiple output coupled complex networks (MOCCNs) under proportional-derivative (PD) and proportional-integral (PI) controllers. Firstly, two classes of MOCCNs without and with external disturbances are separately put forward. Secondly, based on the PD and PI control schemes, several output synchronization criteria for MOCCNs are formulated by using the Lyapunov functional method and inequality techniques. Thirdly, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> output synchronization for MOCCNs is also studied with the help of the PD and PI controllers. Finally, two numerical examples are separately presented to demonstrate the validity of acquired theoretical results.