Consensus of Double-Integrator Multiagent Systems Under Disturbances: Two Types of PI-Based Protocols

This article analyzes the consensus of double-integrator multiagent systems subjected to constant disturbances. First, we propose a proportional–integral (PI)-based consensus protocol with a linear integrator, under which the system can achieve consensus without any steady-state error. By directly analyzing the closed-loop system matrix, a necessary and sufficient condition for parameter selection is derived. Subsequently, to overcome the phase lag defect of the linear integrator, we propose a new PI-based protocol with a split-path nonlinear integrator. The nonlinear consensus protocol can not only ensure that the system achieves asymptotic consensus, but also enhance the transient performance with respect to overshoot. Finally, some simulation comparisons are conducted to validate the effectiveness of the proposed protocols.