Balanced realization and model reduction for unstable systems

This paper proposes a new balanced realization and model reduction method f or possibly unstable systems by introducing some new controllability and ob servability Gramians, These Gramians can be related to minimum control ener gy and minimum estimation error. In contrast to Gramians defined in the lit erature for unstable systems, these Gramians can always be computed for sys tems without imaginary axis poles and they reduce to the standard controlla bility and observability Gramians when the systems are stable. The proposed balanced model reduction method enjoys the similar error bounds as does fo r the standard balanced model reduction, Furthermore, the new error bounds and the actual approximation errors seem to be much smaller than the ones u sing the methods given in the literature for unstable systems. Copyright (C ) 1999 John Wiley & Sons, Ltd.