Stabilizable by a stable and by an inverse stable but not by a stable and inverse stable

The authors disprove conjectures on simultaneous stabilizability conditions by showing that, unlike the case of two plants, the existence of a simultaneous stabilizing controller for more than two plants is not guaranteed by the existence of a controller such that the closed loops have no real unstable poles. An example of a plant which has the even interlacing property but which is not stabilizable by a bistable controller is presented