  Typically when designing distributed controllers it is assumed that the
state-space model of the plant consists of sparse matrices. However, in the
discrete-time setting, if one begins with a continuous-time model, the
discretization process annihilates any sparsity in the model. In this work we
propose a discretization procedure that maintains the sparsity of the
continuous-time model. We show that this discretization out-performs a simple
truncation method in terms of its ability to approximate the "ground truth"
model. Leveraging results from numerical analysis we are also able to
upper-bound the error between the dense discretization and our method.
Furthermore, we show that in a robust control setting we can design a
distributed controller on the approximate (sparse) model that stabilizes the
dense ground truth model.
