This paper proposes a new balanced realization and model reduction method for possibly unstable systems by introducing some new controllability and observability Gramians. These Gramians can be related to minimum control energy and minimum estimation error. In contrast to Gramians defined in the literature for unstable systems, these Gramians can always be computed for systems without imaginary axis poles and they reduce to the standard controllability and observability Gramians when the systems are stable. The proposed balanced model reduction method enjoys the similar error bounds as does for the standard balanced model reduction. Furthermore, the new error bounds and the actual approximation errors seem to be much smaller than the ones using the methods given in the literature for unstable systems.

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