Distributed robust consensus control for multi-agent linear parameter-varying uncertain systems

Distributed robust consensus control problem is investigated for multi-agent systems (MASs) in directed networks with dynamics is dominanted by linear continuous models with polytopic uncertainty. A linear transformation approach is applied, which transforms the state consensus problem of the uncertain MASs into the robust quadratic partial stability problem of a corresponding linear parameter-varying (LPV) system. In doing the linear transformation, an incidence matrix is established as the transformation matrix, which can make the original uncertain system transformed into a reduced-order system. According to this decomposed system, quadratic stabilization system with robust controller is designed. The controller construction mainly relies on solving a finite linear matrix inequalities (LMIs) to approximate, and in the meantime the control gain matrix of the proposed distributed robust consensus protocol is also designed. Finally, the effectiveness of the proposed method is verified by two examples.