Balanced truncation model reduction for systems with inhomogeneous initial conditions

We present a rigorous approach to extend balanced truncation model reduction (BTMR) to systems with inhomogeneous initial conditions, we provide an estimate for the error between the input–output maps of the original and of the reduced initial value system, and we illustrate numerically the superiority of our approach over the naive application of BTMR. When BTMR is applied to linear time invariant systems with inhomogeneous initial conditions, it is crucial that the initial data are well represented by the subspaces generated by BTMR. This requirement is often ignored or it is avoided by making the restrictive assumption that the initial data are zero. To ensure that the initial data are well represented by the BTMR subspaces, we add auxiliary inputs determined by the initial data.