Stabilizing linear time-invariant systems with finite-state hybrid static output feedback

For linear time-invariant (LTI) systems which are not stabilizable by single state feedback or single static output feedback, we consider a hybrid control strategy composed of a finite set of static output feedback controllers and a switching law so that the closed-loop system is asymptotically stable when the controllers are switched under the switching law. Multiple Lyapunov functions and piecewise observers are used to determine the switching law, and a sufficient condition is derived for the existence and the computation of Lyapunov functions and static output feedback gains.