Lag consensus for second-order multi-agent systems with linear or nonlinear coupling via PD and PI control

In this research, the lag consensus problem for second-order nonlinear multi-agent systems (MASs) with linear or nonlinear coupling is studied by employing proportional-derivative (PD) and proportional-integral (PI) control techniques. First, with the suppose of the Lyapunov functional, matrix theory, and elaborate PD controller and PI controller, two sufficient criteria are suggested to assure the lag consensus of linearly coupled MASs. Then the aforesaid findings are expanded to MASs with nonlinear coupling by modifying the above controller and updating the sufficient conditions. Finally, the efficacy of the provided control methodology in different scenarios is manifested through two simulation examples.