A 2-D Realization Theory for Markov Chains
Proceedings of the 29th Conference on Decision and Control
ISSN or ISBN
In this paper we study the dynamics of time homogeneous Markov chain models from a state-space modeling point of view. It is shown that a Markov chain model can be embedded in a 2-D realization theory where markov parameters correspond to higher-order transition probabilities. The implications of formulating a Markov chain model in this state-space domain is that many equivalent representations may exist, some of which may have better robustness properties. A modified Hankel approximation algorithm is presented which exactly matches all the Markov parameters. The algorithm is an extension of the 2-D harmonic retrieval algorithm of D.V.B. Rao et al.
Ramos, Jose A. and Verriest, Erik I., "A 2-D Realization Theory for Markov Chains" (1990). CEC Faculty Articles. 383.