A random time stochastic drift result and application to stochastic stabilization over noisy channels

A random time state-dependent drift result leading to various forms of stochastic stability for a Markov Chain is presented. Application to a network stabilization problem is studied. In particular, we observe that, for control over a discrete erasure channel with feedback, for recurrence or stochastic stability, it suffices to have the capacity being greater than the logarithm of the unstable eigenvalue. For the finiteness of a second moment, however, more stringent criteria are needed.