A simultaneous observer-based controller

In this note, a parametrization of all functional observer-based controllers that stabilize a given plant is proposed. This parametrization is used to design simultaneous functional observer-based controllers for two plants and to derive some sufficient conditions and some necessary conditions for the existence of simultaneous functional observer-based controllers. These sufficient conditions express the existence of simultaneous functional observer-based controllers in function of the unstable zero structure of the difference of the two plants. The necessary conditions set that the existence of simultaneous functional observer-based controllers depends on two Q-parameters. Then, it is shown that the existence conditions of a simultaneous functional observer-based controller are not exactly a simple concatenation of the existence conditions of a simultaneous controller and the existence conditions of a simultaneous functional observer. Finally, a design procedure to compute simultaneous functional observer-based controllers is presented.