Quadratic stabilizability and H_∞ disturbance attenuation of switched linear systems via state and output feedback

We consider quadratic stabilizability and H_∞ disturbance attenuation of switched systems which are composed of a finite set of linear time-invariant subsystems. The situation is that none of the subsystems is quadratically stable with certain H_∞ disturbance attenuation level but a convex combination of the subsystems achieves such performance. We then design a state-dependent switching signal (state feedback) and an output-dependent switching signal (output feedback) such that the entire switched system is quadratically stable with the same H_∞ disturbance attenuation level. In the case of state feedback, when the number of subsystems is two, we show that the existence of desired convex combination of subsystems is not only sufficient but also necessary for quadratic stabilizability with the H_∞ disturbance attenuation of the switched system.