Containment control of linear multi-agent systems with directed graphs and multiple leaders of time-varying bounded inputs

This study addresses containment control problem for multi-agent systems with general linear dynamics. The main contribution of this study is to solve the containment control problem with multiple leaders whose control inputs might be non-zero, time varying, and the interaction graph among the followers is directed. On the basis of the neighbouring state information, a distributed static containment controller is designed, the containment error asymptotically converges to zero if the subgraph associated with the followers is directed and at least one leader has a directed path to each follower. Then, an observer-based adaptive containment controller is proposed without knowing any global information about the topology, especially the eigenvalues of the Laplacian matrix. Simulations indicate the capabilities of the algorithm.