Model Reduction for Robust Control: A Schur Relative-Error Method

A numerically robust Relative Error Method (REM) for state-space model order reduction is described. Our algorithm is based on Desai's Balanced Stochastic Truncation (BST) technique for which M. Green has obtained an L∞ relative-error bound. However, unlike previous methods, our Schur method completely circumvents the numerically delicate initial step of obtaining a minimal balanced stochastic realiztion (BSR) of the the power spectrum matrix G(s)GT(-s).