Output agreement in networks with unmatched disturbances and algebraic constraints

This paper considers a problem of output agreement in heterogeneous networks with dynamics on the nodes as well as on the edges. The control and disturbance signals entering the nodal dynamics are "unmatched" meaning that some nodes are only subject to disturbances, and are deprived of actuating signals. To further enrich our model, we accommodate (solvable) algebraic constraints in a subset of nodal dynamics. We show that appropriate dynamic feedback controllers achieve output agreement on a desired vector. We also investigate the case of an optimal steady-state control over the network. The proposed results are applied to a heterogeneous microgrid.