  We consider the problem of output feedback controller sparsification for
systems with parametric uncertainties. We develop an optimization scheme that
minimizes the performance deterioration caused by the sparsification process,
while enhancing sparsity pattern of the feedback gain. In order to improve
temporal proximity of an existing closed-loop system and its sparsified
counterpart, we also incorporate an additional constraint into the problem
formulation so as to bound the variation in the system output pre and post
sparsification. We also show that the resulting non-convex optimization problem
can be equivalently reformulated into a rank-constrained optimization problem.
We then formulate a bi-linear minimization program along with an iterative
algorithm to obtain a sub-optimal solution which satisfies the rank constraint
with arbitrary tolerance. Lastly, a sub-optimal sparse controller design for
IEEE 39-bus New England power network is utilized to showcase the effectiveness
of our proposed method.
