  We study a sampled-data implementation of linear controllers that depend on
the output and its derivatives. First, we consider an LTI system of relative
degree $r\ge 2$ that can be stabilized using $r-1$ output derivatives. Then, we
consider PID control of a second order system. In both cases, the Euler
approximation is used for the derivatives giving rise to a delayed sampled-data
controller. Given a derivative-dependent controller that stabilizes the system,
we show how to choose the parameters of the delayed sampled-data controller
that preserves the stability under fast enough sampling. The maximum sampling
period is obtained from LMIs that are derived using the Taylor's expansion of
the delayed terms with the remainders compensated by appropriate
Lyapunov-Krasovskii functionals. Finally, we introduce the event-triggering
mechanism that may reduce the amount of sampled control signals used for
stabilization.
