Derivative-free data-driven control of continuous-time linear time-invariant systems

This paper develops a method for data-driven stabilization of continuous-time linear time-invariant systems with theoretical guarantees and no need for signal derivatives. The framework is based on linear matrix inequalities (LMIs) and illustrated in the state-feedback and single-input single-output output-feedback scenarios. Similar to discrete-time approaches, we rely solely on input and state/output measurements. In particular, we avoid differentiation by employing low-pass filters of the measured signals that, rather than approximating the derivatives, reconstruct a non-minimal realization of the plant. With access to the filter states and their derivatives, we can solve LMIs derived from sample batches of the available signals to compute a dynamic controller that stabilizes the plant. The effectiveness of the approach is showcased via numerical examples.