A bstract-The calculation of the balancing transformation required in Moore's "balanced-truncation" model reduction procedure for stable systems tends to be badly conditioned, especially for nonminimal models that stand to benefit the most from model reduction. In this note it is shown that a not-necessarily-balanced state-space realization of the Moore reduced model can be computed directly without balancing via projections defined in terms of arbitrary bases for the left and right eigenspaces associated with the "large" eigenvalues of the product PQ of the reachability and controllability Grammians. Two specific methods for computing these bases are proposed, one based on the ordered Schur decomposition of P Q and the other based on the Cholesky factors of P and Q. The algorithms perform reliably even for nonminimal models.

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