Output Feedback Stabilization of Polynomial State-Affine Control Systems Using Control Templates

We establish a separation principle for the output feedback stabilization of state-affine systems that are observable at the stabilization target. Relying on control templates [recently introduced in Andrieu et al. (2024)], that allow to approximate a feedback control while maintaining observability, we design a closed-loop hybrid state-observer system that we show to be semi-globally asymptotically stable. Under assumption of polynomiality of the system with respect to the control, we give an explicit construction of control templates. We illustrate the results of this letter with numerical simulations.