Improved sampled-data implementation of derivative-dependent control

We consider an LTI system of relative degree two that can be stabilized using the output and its derivative. The derivative is approximated using a finite difference, what leads to a time-delayed feedback. This feedback is analyzed using a Lyapunov-Krasovskii functional that compensates the derivative approximation error presented in an integral form. We show that if the derivative-dependent control exponentially stabilizes the system, then one can use consecutively sampled measurements to approximate the derivative and this approximation will preserve the stability if the sampling period is small enough. We provide linear matrix inequalities that allow to find admissible sampling period and can be used for robustness analysis with respect to system uncertainties. The results are demonstrated by two examples: 2D uncertain system and the Furuta pendulum.