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Balanced realization and model reduction for unstable systems. (English) Zbl 0949.93018
By means of examples the authors show that the balanced realizations defined in the existing literature are not appropriate for unstable systems.
Therefore the authors introduce and analyze new definitions of observability and controllability gramians.
These gramians are then related to the issues of balanced realization and model reduction for unstable systems where the state matrix $$A$$ has no eigenvalues on the imaginary axis.
This paper is well written and illustrated by some examples.

MSC:
 93B20 Minimal systems representations 93B11 System structure simplification
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