  We study a linear quadratic regulation problem with a constraint where the
control input can be nonzero only at a limited number of times. Given that this
constraint leads to a combinational optimization problem, we adopt a greedy
method to find a suboptimal solution. To quantify the performance of the greedy
algorithm, we employ two metrics that reflect the submodularity level of the
objective function: The submodularity ratio and curvature. We first present an
explicit form of the optimal control input that is amenable to evaluating these
metrics. Subsequently, we establish bounds on the submodularity ratio and
curvature, which enable us to offer a practical performance guarantee for the
greedy algorithm. The effectiveness of our guarantee is further demonstrated
through numerical simulations.
