Mean square stabilizability of linear systems with limited feedback data rates and Markovian packet losses

This paper studies the mean square stabilizability of linear discrete-time systems over a lossy digital communication channel. The packet losses process of the channel is modeled as a time-homogeneous binary Markov process. The temporal correlations of the channel and stochastically time-varying data rate due to packet losses pose a significant challenge, which is solved by developing a randomly sampled system approach. It is shown that the number of additional bits to counter effects of the Markovian packet losses on stabilizability is exactly quantified by the magnitude of the unstable mode and the transition probabilities. Our result contains existing results on data rate and packet dropout rate for stabilizability of linear systems as special cases. Necessary and sufficient conditions on the minimum data rate problem for vector systems are also provided respectively and shown to be optimal for some special cases.