Dynamic Quantizers in Presence of Noisy Channels

In this paper, we deal with the stabilizability of a scalar plant through a noisy discrete channel. Our scheme can be regarded as a variation of the controllers based on dynamic quantizers introduced in [3] and [4], but our analysis based on Lyapunov function allows us to take into consideration more general discrete memoryless channels. Given a plant and a discrete memoryless channel we will provide, using control Lyapunov function ideas, a condition for the existence of an encoder/controller pair with a priori fixed memory that achieves stability. A construction procedure is also provided.