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This paper considers the open problem whether there exists a finite-state hybrid output feedback control to asymptotically stabilize a second-order linear dynamic system. More precisely, for second-order linear time-invariant systems which are not stabilizable via a single static output feedback, we find two different output feedback gains and a switching law orchestrating the feedback gains such that the closed-loop system is asymptotically stable.

Stabilizing Second-Order Linear Dynamic Systems Via Hybrid Output Feedback Controls