Stabilization of uncertain systems with finite data rates and Markovian packet losses

Abstract

This research addresses stabilization of uncertain systems over data rate constrained and lossy channels. While many of the existing works assume that the packet loss process is independent and identically distributed, we model it as a two-state Markov chain, which can deal with more practical situations including bursty dropouts. For parametrically uncertain plants, a necessary condition and a sufficient condition for mean square stability are derived. These conditions are represented by the product of the eigenvalues of the nominal plants, the data rate, the transition probabilities of the channel states, and the upper bounds of uncertainties. In particular, for scalar plants, the conditions coincide with each other.