Stochastic balancing and approximation - Stability and minimality

A new method of balancing, called stochastic balancing, has recently been introduced. This paper focuses on the stability aspects of the associated stochastic model reduction scheme. It is shown that in both the continuous-time and discrete-time cases the reduced order model is asymptotically stable and dissipative. Further, it is shown that in the continuous-time case the reduced order model is minimal.