Output containment via multi-consensus for heterogeneous linear systems on digraphs

In this paper we show how the problem of containment on arbitrary output trajectories for a group of linear systems connected by a digraph can be analyzed and solved based on topological results on multi-consensus concerning the network structure. Specifically, we apply this approach to the case of heterogeneous agents, for which output containment is the relevant task. We assume that each agent only measures the output of the corresponding exosystem, that defines the consensus trajectory. Indeed, the latter one is asymptotically generated by a set of linear systems (the exosystems) suitably exchanging information through the network. The approach proposed allows for the distributed, consensus-based stabilization of the containment dynamics without requiring the agents to have any non-local knowledge of the network structure.