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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 <inline-formula><tex-math notation="LaTeX">$r\geq 2$</tex-math> </inline-formula> that can be stabilized using <inline-formula><tex-math notation="LaTeX">$r-1$</tex-math> </inline-formula> 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 Taylor&#x0027;s expansion of the delayed terms with the remainders compensated by appropriate Lyapunov&#x2013;Krasovskii functionals. Finally, we introduce the event-triggering mechanism that may reduce the amount of sampled control signals used for stabilization.

Sampled-Data Implementation of Derivative-Dependent Control Using Artificial Delays