Approximation and limiting behavior of random models

In this paper, we investigate limiting behavior of linear dynamic systems driven by random stochastic matrices. We introduce and study the new concepts of partial ergodicity and 1-approximation of a given chain of stochastic matrices. We show that partial ergodicity of a chain is invariant under 1-approximations. We also introduce an infinite flow graph of a random chain and use the connectivity components of this graph to characterize the ergodicity classes of a chain. Finally, we provide a result showing that, under certain conditions, the ergodicity classes of an independent random chain and its expected counterpart are the same.

• Type: Journal
• Year: 2010
• Where: CDC
• Authors: Behrouz Touri, Angelia Nedic
• Keywords: CDC 2010, Chain, Control Systems, Random Chain, Stochastic Matrices