Output synchronization of linear MIMO heterogeneous multi-agent systems via output communication

The output synchronization of heterogeneous multi-agent systems becomes more challenging when only output information is exchanged over the network rather than state information. We showed that the problem can be solved in two mutually coupled steps, namely perturbed consensus which is closely related to the well solved synchronization of homogeneous multi-agent systems and perturbed regulation which for MIMO systems is of particular interest. The perturbed regulation problem takes the consensus error of homogeneous reference model constructed for each agent as the disturbance while its regulation error also enters into the perturbed consensus problem as the disturbance. As opposed to traditional regulation problem, we aim to render the gain from the consensus error to the regulation error satisfy a small-gain condition at the second step. Based on the controllability property, we establish a lemma that derives a bound condition for the solution to a class of Riccati equations. Applying the lemma, we propose state and dynamic output feedback controllers to solve perturbed regulation problem and hence the output synchronization problem for linear MIMO multi-agent systems.