Stabilizing a harmonic oscillating system with hybrid output feedback controls

This paper presents a hybrid static output feedback stabilization approach for harmonic oscillating systems, which are not stabilized via a single static output feedback. More precisely, we find two output feedback control gains and a switching law orchestrating the feedback gains such that the deduced closed-loop switched system is asymptotically stable. Based on a new sufficient condition for stabilization of second-order switched linear systems, under the predetermined "most stabilizing" switching law which is a time-controlled switching, it is shown that stability conditions can be met with respect to the discrete state when the switched system's stabilization theorem is used.