Abstract
The balanced stochastic realization is introduced as a balanced solution to the continuous time positive real equations and the dual positive real equations. The structure of the associated balanced spectral factors is derived, the main result being a product decomposition of the spectral factors. The properties of the stochastic model reduction technique of balanced stochastic truncation are considered. In particular it is shown that balanced stochastic truncation preserves the right half plane zeros of the spectral factors, leading to a transformation approach to the approximation of non-minimum-phase stochastic systems.
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