Quadratic stabilizability of discrete-time switched systems via state and output feedback

We study quadratic stabilizability via state and output feedback for switched systems composed of several discrete-time linear time-invariant subsystems, under the assumption that all subsystem matrices are unstable. We derive a sufficient condition expressed as a matrix inequality under which the switched system is quadratically stabilizable via a state-based switching strategy, and we show that the sufficient condition is also necessary if the number of subsystems is two. When a robust detectability condition is satisfied in addition to the sufficient condition, we construct a quadratically stabilizing switching strategy based on the measurement output.