A brief note on the generalized singular perturbation approximation

The generalized singular perturbation approximation is a method for approximation of dynamical systems which has been presented in the literature on model reduction over the past two decades. In this note, the generalized singular perturbation approximation is studied and it is shown that this order reduction method is not always true and may leads to inaccurate results and is therefore erroneous. This conclusion holds for the extended methods such as the parametric generalized singular perturbation approximation or the recently presented dissipativity-preserving model reduction based on generalized singular perturbation.