Balancing free square-root algorithm for computing singular perturbation approximations

Abstract

The author proposes a novel algorithm with enhanced numerical robustness for computing singular perturbation approximations of linear, continuous or discrete systems. This algorithm circumvents the computation of possibly ill-conditioned balancing transformations. Instead, well-conditioned projection matrices are determined for computing state-space representations suitable for applying the singular perturbation formulas. The projection matrices are computed using the Cholesky (square-root) factors of the gramians. The proposed algorithm is intended for efficient computer implementation. It can handle both minimal and nonminimal systems.<>