Synchronization in networks of linear agents with output feedbacks

The problem is considered of asymptotic synchronization by states in networks of identical linear agents in the application of the consensual output feedback. For the networks with fixed topology and without delay in the information transmission, on the basis of the passification theorem and the Agaev–Chebotarev theorem, the possibility is established of the provision of synchronization (consensus) of strong feedback under the assumption of the strict passification of agents and the existence of the incoming spanning tree in the information graph. In contrast to the known works, in which only the problems with the number of controls equal to the number of variables of the state of agents are investigated, in this work a substantially more complex case is considered, where the number of controls is less than the number of variables of the state, namely: the control is scalar. The results are illustrated by the example for the ring-shaped network of four dual integrators.