  In this paper, we consider networked systems comprised of interconnected sets
of linear subsystems and propose a decentralized and compositional approach to
stabilize or dissipativate such linear networked systems via optimally
modifying some existing interconnections and/or creating entirely new
interconnections. We also extend this interconnection topology synthesis
approach to ensure the ability to stabilize or dissipativate such linear
networked systems under distributed (local) feedback control. To the best of
the authors' knowledge, this is the first work that attempts to address the
optimal interconnection topology synthesis problem for linear networked
systems. The proposed approach in this paper only involves solving a sequence
of linear matrix inequality problems (one at each subsystem). Thus, using
standard convex optimization toolboxes, it can be implemented efficiently and
scalably in a decentralized and compositional manner. Apart from many generic
linear networked systems applications (e.g., power grid control), a unique
application for the proposed interconnection topology synthesis approach is in
generating random stable (or dissipative, stabilizable, dissipativate-able)
linear networked systems for simulation purposes. We also include an
interesting case study where the proposed interconnection topology synthesis
approach is compared with an alternative approach that only uses dissipativity
information of the involved subsystems.
