Output feedback stabilisation of bilinear systems via control templates

We establish a separation principle for the output feedback stabilisation of state-affine systems that are observable at the stabilization target. Relying on control templates (recently introduced in [4]), 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 the paper with numerical simulations.