Containment control for the cooperative output regulation of linear multi-agent systems

In this paper, the containment control problem is studied for the cooperative output regulation of linear multi-agent systems(MASs). The output regulation problem initiated from single-leader-follower region is extended to the multi-leadersfollower region. The purpose of this paper is to design a containment control algorithm such that all the followers can move into the convex hull formed by the leaders. A sufficient and necessary condition in term of a linear matrix inequality (LMI) is derived for the existence of a containment controller protocol that guarantees the followers are capable to follow the trail of leader and the output error will converge to zero with the time elapsing. Then, a controller design procedure is given to construct the feedback gain matrix and select the proper gain matrix for achieving final consensus of the MASs. Compared with the existing algorithms, the proposed one requires less information and calculation of the velocities measurement of the agents. Finally, a numerical example is illustrated to show the usefulness of the designed containment controller.