  We study a class of dynamical networks modeled by linear and time-invariant
systems which are described by state-space realizations. For these networks, we
investigate the relations between various types of factorizations which
preserve the structure of their component subsystems' interconnection. In doing
so, we provide tractable means of shifting between different types of
sparsity-preserving representations and we show how to employ these
factorizations to obtain distributed implementations for stabilizing and
possibly stable controllers. By formulating all these results for both
discrete- and continuous-time systems, we develop specialized distributed
implementations that, up to this point, were only available for networks
modeled as discrete-time systems.
