1On Rates of Convergence for Markov Chains under Random Time State Dependent Drift Criteria

Abstract—Many applications in networked control require intermittent access of a controller to a system, as in event-triggered systems or information constrained control applica-tions. Motivated by such applications and extending previous work on Lyapunov-theoretic drift criteria, we establish both subgeometric and geometric rates of convergence for Markov chains under state dependent random time drift criteria. We quantify how the rate of ergodicity, nature of Lyapunov functions, their drift properties, and the distributions of stopping times are related. We finally study an application in networked control. I. INTRODUCTION AND LITERATURE REVIEW Stochastic stability of Markov chains has an almost com-plete theory, and forms a foundation for several other general techniques such as dynamic programming, linear programmin