Static output feedback of equivariant linear systems with applications to the control of interconnected agents

We focus on controlled linear systems which are invariant with respect to a set of linear transformations associated to a general multiplicative finite group G. We investigate their control theoretical properties of stability, stabilizability, detectability and output feedback stabilizability. We apply the obtained results to systems obtained by the interconnection of identical subsystems, exploiting their invariance with respect to the group of the automorphisms of the connection graph.