Stability criteria for Arnoldi-based model-order reduction

Pade approximation is an often-used method for reducing the order of a finite-dimensional, linear, time invariant, signal model. It is known to suffer from two problems: numerical instability during the computation of the Pade coefficients and lack of guaranteed stability for the resulting reduced model even when the original system is stable. We show how the numerical instability problem can be avoided using the Arnoldi algorithm applied to an appropriately chosen Krylov subspace. Moreover, we give an easily computable sufficient condition on the system matrix that guarantees the stability of the reduced model at any approximation order