Hybrid output feedback stabilization of two-dimensional linear control systems

We solve for two-dimensional SISO linear control systems the open problem whether there exists finite-state hybrid output feedback to stabilize the systems. We show that under reasonable assumptions, such as stabilizability and detectability conditions, the answer to this question is affirmative for the case of 2-state output feedback. We also address a simulation procedure to locate the stabilizable regions for switched systems consisting of two subsystems. We demonstrate the applicability of our results by considering several specific examples.