PID Control for Output Synchronization of Multiple Output Coupled Complex Networks

Abstract

This article attempts to address output synchronization and <inline-formula><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><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.