  This paper studies the problem of selecting a minimum-size set of input nodes
to guarantee stability of a networked system in the presence of uncertainties
and time delays. Current approaches to input selection in networked dynamical
systems focus on nominal systems with known parameter values in the absence of
delays. We derive sufficient conditions for existence of a stabilizing
controller for an uncertain system that are based on a subset of system modes
lying within the controllability subspace induced by the set of inputs. We then
formulate the minimum input selection problem and prove that it is equivalent
to a discrete optimization problem with bounded submodularity ratio, leading to
polynomial-time algorithms with provable optimality bounds. We show that our
approach is applicable to different types of uncertainties, including additive
and multiplicative uncertainties in the system matrices as well as uncertain
time delays. We demonstrate our approach in a numerical case study on the IEEE
39-bus test power system.
