Robust switching of discrete-time switched linear systems

In this work, we address the problem of robust switching design, which seeks a switching signal that makes the switched system exponentially stable and robust against switching perturbations. To properly capture the sensitivity of a switching signal undergoing various switching perturbations, we define the relative distance between state-feedback path-wise switching signals. We establish that any stabilizing state-feedback path-wise switching signal is robust with respect to switching perturbations. A lower bound of the robustness margin is explicitly presented.