PD and PI Control for the Lag Consensus of Nonlinear Multiagent Systems With and Without External Disturbances

In this article, we investigate the lag consensus and lag
$\mathcal {H}_{\infty }$
consensus problems for second-order nonlinear multiagent systems (MASs) by utilizing the proportional-derivative (PD) and proportional-integral (PI) control methods. On the one hand, a criterion is developed for ensuring the lag consensus of the MAS by choosing an appropriate PD control protocol. Moreover, a PI controller is also provided to guarantee that the MAS can achieve lag consensus. On the other hand, several lag
$\mathcal {H}_{\infty }$
consensus criteria are also given for the case in which external disturbances appear in the MAS; these criteria are developed by exploiting the PD and PI control strategies. Finally, the devised control schemes and the developed criteria are verified by employing two numerical examples.