Robust consensus control for a class of multi-agent systems via distributed PID algorithm and weighted edge dynamics

This paper studies the robust proportional-integral-derivative (PID) consensus control for a class of linear multi-agent systems (MASs) with external disturbances. Different from the existing results, both the consensus analysis and the transient performance characteristics for high-order linear MASs are considered. Based on a factorization of Laplacian matrix, the initial MAS is firstly transformed into the so-called weighted edge dynamics, and then a design equivalence between the proposed PID consensus controller and the corresponding stabilizing controller for such weighted edge dynamics is presented via some graph theory results. Furthermore, by combining Lyapunov theory and Barbalat's Lemma, it is proved that both the stabilization of weighted edge dynamics and the consensus of MAS can be guaranteed even in the presence of external disturbances. In particular, some relationships between the transient time performance of weighted edge dynamics and the PID design parameters are given. Finally, some numerical examples on LC oscillator network are provided to illustrate the validity of theoretical results.