  We study networks with linear dynamics where the presence of symmetries of
the pair (A,B) induces a partition of the network nodes in clusters and the
matrix A is not restricted to be in Laplacian form. For these networks, an
invariant group consensus subspace can be defined, in which the nodes in the
same cluster evolve along the same trajectory in time. We prove that the
network dynamics is uncontrollable in directions orthogonal to this subspace.
Under the assumption that the dynamics parallel to this subspace is
controllable, we design optimal controllers that drive the group consensus
dynamics towards a desired state. Then, we consider the problem of selecting
additional control inputs that stabilize the group consensus subspace and
obtain bounds on the minimum number of additional inputs and driver nodes
needed to this end. Altogether, our results indicate that it is possible to
design independently the control action along and transverse to the group
consensus subspace.
