Stochastic balancing and approximation-stability and minimality

A new method of stochastic model reduction has recently been introduced by Desai et al. 1], 2]. The stability of the reduced order model has not previously, been considered. In this paper, we show that the stability of the reduced order model follows directly from the results of Pernebo and Silverman 3]. It is also shown that the reduced order model is minimal, in the controllability/observability sense. The relevance of this notion of minimality to stochastic minimality is made clear.