Stabilization of Discrete-time Linear Systems via Quantized Signals with Packet Losses

In this paper, we consider to derive the coarsest memory-less quantizer which can stabilize a single-input discrete-time linear time-invariant system with stochastic packet losses in the sense of stochastic quadratic stability. We show that the upper bound of the coarseness is strictly given by the packet loss probability and the unstable poles of the plant. We furthermore deal with permissible dead-band width around the origin of the quantizers and time-varying finite quantizers in order to realize control using finite communication rate.