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

Authors:
Serdar Yüksel
Affiliations:
Mathematics and Engineering Program, Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, Canada
Venue:
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Year:
2009

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Abstract

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.