Model reduction via balancing, and connections with other methods

This paper starts with a rather philosophical viewpoint on the concepts of modeling, model reduction, and randomness. The theory of open-loop deterministic balancing is introduced as a particular implementation of a model reduction scheme. The discussion focusses on the choice of the criterion. Thus motivated, it is shown that similar ideas can be employed in the reduction of optimally controlled systems under the presence of noise, leading to the LQG-balanced realizations. This connects to the stochastic balanced realizations. Finally, different stochastic realization algorithms are cast in the common framework of the RV-coefficient, and the deeper geometric significance of this measure is explored.

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