  This work is associated with the use of parallel feedforward compensators
(PFCs) for the problem of output synchronization over heterogeneous agents and
the benefits this approach can provide. Specifically, it addresses the addition
of stable PFCs on agents that interact with each other using diffusive
couplings. The value in the application of such PFC is twofold. Firstly, it has
been an issue that output synchronization among passivity-short systems
requires global information for the design of controllers in the cases when
initial conditions need to be taken into account, such as average consensus and
distributed optimization. We show that a stable PFC can be designed to
passivate a passivity-short system while its output asymptotically vanishes as
its input tends to zero. As a result, output synchronization is achieved among
these systems by fully distributed controls without altering the original
consensus results. Secondly, in the literature of output synchronization over
signed weighted graphs, it is generally required that the graph Laplacian be
positive semidefinite, i.e., $L \geq 0$ for undirected graphs or $L + L^T \geq
0$ for balanced directed graphs. We show that the PFC serves as output feedback
to the communication graph to enhance the robustness against negative weight
edges. As a result, output synchronization is achieved over a signed weighted
and balanced graph, even if the corresponding Laplacian is not positive
semidefinite.
