  In this paper we study state-space realizations of Linear and Time-Invariant
(LTI) systems. Motivated by biochemical reaction networks, Gon\c{c}alves and
Warnick have recently introduced the notion of a {\em Dynamical Structure
Functions} (DSF), a particular factorization of the system's transfer function
matrix that elucidates the interconnection structure in dependencies between
manifest variables. We build onto this work by showing an intrinsic connection
between a DSF and certain sparse left coprime factorizations. By establishing
this link, we provide an interesting systems theoretic interpretation of
sparsity patterns of coprime factors. In particular we show how the sparsity of
these coprime factors allows for a given LTI system to be implemented as a
network of LTI sub-systems. We examine possible applications in distributed
control such as the design of a LTI controller that can be implemented over a
network with a pre-specified topology.
