A balanced model reduction method for a class of matrix inversion problems with parametric uncertainty

A model reduction method is proposed for parameter-dependent matrix inversion problems, in which the matrix entries are rational functions of the parameters. Its goal is to reduce the complexity of symbolic expressions that appear in the inverse, taking into account parametric uncertainty. The complexity reduction and its error bound are based on existing balanced model reduction techniques for linear fractional transformations. The method is applied to system matrices that arise from the modeling of electrical networks.