Canonical Variate Modeling and Approximation of Linear Systems
This paper treats balanced realization problems within the framework of canonical variate analysis. By applying the concepts of statistical studies, duality diagrams, and the RV-coefficient to deterministic systems, it is shown how both the identification (Hankel approach) and transformation (Grammian approach) based balanced realization problems lead to dual interpretations. It is further shown that both approaches lead to a minimum distance problem (equivalently maximum RV-coefficient) between certain observability and controllability properties of a linear system. The motivation for this optimization problem follows from the singular value decomposition, the orthogonal procrustes problem, and the RV-coefficient. The solution has the format of a generalized singular value decomposition.
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