Stability of feedback switched systems with state and switching delays

We study stability of state feedback switched systems in which time delays are present in both the feedback state and the switching signal of the controller. For switched linear systems with average dwell-time switching signals, we provide a condition in terms of upper bounds on the delays and a lower bound on the average dwell-time to guarantee asymptotic stability of the closed loop. Our approach employs multiple Lyapunov functions and the merging switching signal technique. We then apply our stability results in switched systems to consensus networks with asymmetric time-varying delays and switching topologies.