Stabilizing a switched linear system by sampled-data quantized feedback

We study the problem of asymptotically stabilizing a switched linear control system using sampled and quantized measurements of its state. The switching is assumed to be slow enough in the sense of combined dwell time and average dwell time, each individual mode is assumed to be stabilizable, and the available data rate is assumed to be large enough. Our encoding and control strategy is rooted in the one proposed in our earlier work on non-switched systems, and in particular the data-rate bound used here is the data-rate bound from that earlier work maximized over the individual modes. The main technical step that enables the extension to switched systems concerns propagating over-approximations of reachable sets through sampling intervals, during which the switching signal is unknown.