A New Square-root Balancing-Free Stochastic Truncation Model Reduction Algorithm

Abstract

The paper proposes a new computational approach with enhanced numerical robustness for computing reduced order models of continuous systems by using the balanced stochastic truncation model reduction method. The new approach circumvents the computation of possibly III-conditioned stochastic balancing transformations. Instead, well-conditioned projection matrices are determined for computing directly the state-space representations of the reduced order models. The projection matrices are computed in a numerically reliable way, by using exclusively the Cholesky (square-root) factors of systems Gramians. The proposed algorithm can handle both minimal and non-minimal systems.