A model reduction problem of certain large-scale Markov chains under an optimal criterion for Hankel-norm approximation is discussed. The multi-dimensional Markov chain under investigation is assumed to have a finite-dimensional stationary state-transition matrix, which is first reformulated as a multi-input/multi-output (MIMO) linear time-invariant (LT1) stochastic system. Consequently, the resulting large-scale MIMO LTI stochastic system has a closed-form best approximant in the Hankel-norm from a specified class of stable lower-dimensional MIMO LTI systems.
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