Data-driven control of continuous-time systems: A synthesis-operator approach

This paper addresses data-driven control of continuous-time systems. We develop a framework based on synthesis operators associated with input and state trajectories. A key advantage of the proposed method is that it does not require the state derivative and uses continuous-time data directly without sampling or filtering. First, systems compatible with given data are described by the synthesis operators into which data trajectories are embedded. Next, we characterize data informativity properties for system identification and for stabilization. Finally, we establish a necessary and sufficient condition for informativity for quadratic stabilization in the presence of process noise. This condition is formulated as linear matrix inequalities by exploiting the finite-rank structure of the synthesis operators.