Feedback stabilization of switched delay systems under data rate constraints

We consider the stabilization problem of a switched delay system using sampled and quantized measurements of its state which result in finite data-rate communication. We assume that the switching is subject to the slow-switching. Each individual subsystem is assumed to be stabilizable. We derive a relationship between the number of values taken by the quantizer and the transition matrix of each individual open-loop system over one sampling period, which achieves the global asymptotic stabilization.