  We consider a discrete-time linear system for which the control input is
updated at every sampling time, but the state is measured at a slower rate. We
allow the state to be sampled according to a periodic schedule, which dictates
when the state should be sampled along a period. Given a desired average
sampling interval, our goal is to determine sampling schedules that are optimal
in the sense that they minimize the $h_2$ or the $h_\infty$ closed-loop norm,
under an optimal state-feedback control law. Our results show that, when the
desired average sampling interval is an integer, the optimal state sampling
turns out to be evenly spaced. This result indicates that, for the $h_2$ and
$h_\infty$ performance metrics, there is relatively little benefit to go beyond
constant-period sampling.
