Hybrid Static Output Feedback Stabilization of Two-Dimensional LTI Systems: A Geometric Method

For two-dimensional linear time-invariant (LTI) systems which are not stabilizable via a single static output feedback, we propose a hybrid stabilization strategy based on a geometric method. More precisely, we design two static output feedback gains and a switching law between the feedback gains so that the entire closed-loop system is asymptotically stable. The proposed switching law is composed of output-dependent switching and time-controlled switching. We demonstrate the design method with various examples, and show that in some cases the stabilizability depends on the region of the initial state, while in other cases the system is globally stabilizable.