Distributed containment control of linear multi-agent systems with multiple leaders of bounded unknown inputs

This paper considers the distributed containment control problem for multi-agent systems with general linear dynamics and multiple leaders whose control inputs are possibly nonzero and not available to any follower. It is assumed that the communication graph among the followers is undirected, there exists at least one leader that has a directed path to each follower, and the leaders' control inputs are bounded. Based on the relative state information of neighboring agents, two distributed controllers with, respectively, static and adaptive coupling gains, are designed to solve the containment control problem, i.e., the states of the followers asymptotically converge to the convex hull formed by those of the leaders. A sufficient condition for the existence of these distributed controllers is that each agent is stabilizable. A simulation example is given to illustrate the theoretical results.