Random-Time, State-Dependent Stochastic Drift for Markov Chains and Application to Stochastic Stabilization Over Erasure Channels
It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of stochastic networks. In this paper we extend the general...
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| Veröffentlicht in: | IEEE transactions on automatic control 2013-01, Vol.58 (1), p.47-59 |
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| creator | Yuksel, S. Meyn, S. P. |
| description | It is known that state-dependent, multi-step Lyapunov bounds lead to greatly simplified verification theorems for stability for large classes of Markov chain models. This is one component of the "fluid model" approach to stability of stochastic networks. In this paper we extend the general theory to randomized multi-step Lyapunov theory to obtain criteria for stability and steady-state performance bounds, such as finite moments. These results are applied to a remote stabilization problem, in which a controller receives measurements from an erasure channel with limited capacity. Based on the general results in the paper it is shown that stability of the closed loop system is assured provided that the channel capacity is greater than the logarithm of the unstable eigenvalue, plus an additional correction term. The existence of a finite second moment in steady-state is established under additional conditions. |
| doi_str_mv | 10.1109/TAC.2012.2204157 |
| format | Article |
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Based on the general results in the paper it is shown that stability of the closed loop system is assured provided that the channel capacity is greater than the logarithm of the unstable eigenvalue, plus an additional correction term. The existence of a finite second moment in steady-state is established under additional conditions.</description><subject>Algorithms</subject><subject>Asymptotic stability</subject><subject>Channels</subject><subject>Computational fluid dynamics</subject><subject>Eigenvalues</subject><subject>Information theory</subject><subject>Markov chain Monte-Carlo (MCMC)</subject><subject>Markov chains</subject><subject>Markov processes</subject><subject>Mathematical analysis</subject><subject>networked control systems</subject><subject>Noise</subject><subject>Stability</subject><subject>Stability criteria</subject><subject>Stabilization</subject><subject>Steady-state</subject><subject>stochastic stability</subject><subject>Stochasticity</subject><subject>Studies</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNpdkU1LJDEQhoOs4Kx6F7wE9uLBHvPZSR-H8WMXFEHn3qTT1RjtSdokI6w3_7kZRpbFU_FSz1MUvAidUDKnlDQXq8Vyzghlc8aIoFLtoRmVUldMMv4DzQihumqYrg_Qz5SeS6yFoDP08WB8H9bVyq3hHD9mk6G6hAl8Dz6XHOyTSdlZfBndkPEQIr4z8SW84eWTcT7houPFNI3OmuyCxzn8b5WDnRvd-253_wYRX0WTNhG2vvcwpiO0P5gxwfHXPESr66vV8nd1e3_zZ7m4rSyv61z1ttZKSTkQMljSdFyQpu8HbXRnQXHe867TWklhtTaGWSasslp2XceL0PBDdLY7O8XwuoGU27VLFsbReAib1FKmeS0UE6qgv76hz2ETfXmuUEJIqZQihSI7ysaQUoShnaJbm_i3paTdVtKWStptJe1XJUU53SkOAP7hNaOSMM4_AXNLiJE</recordid><startdate>201301</startdate><enddate>201301</enddate><creator>Yuksel, S.</creator><creator>Meyn, S. 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| source | IEEE Electronic Library (IEL) |
| subjects | Algorithms Asymptotic stability Channels Computational fluid dynamics Eigenvalues Information theory Markov chain Monte-Carlo (MCMC) Markov chains Markov processes Mathematical analysis networked control systems Noise Stability Stability criteria Stabilization Steady-state stochastic stability Stochasticity Studies |
| title | Random-Time, State-Dependent Stochastic Drift for Markov Chains and Application to Stochastic Stabilization Over Erasure Channels |
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