Setpoint control of bilinear systems from noisy data

We consider the problem of designing a controller for an unknown bilinear system using only noisy input-states data points generated by it. The controller should in principle achieve regulation to a given state setpoint and provide a guaranteed basin of attraction. Determining the equilibrium input to achieve that setpoint is not trivial in a data-based setting and we propose the design of a controller in two scenarios. The design takes the form of linear matrix inequalities and is validated numerically for a Ćuk converter.