A Real Schur Form Method for Modeling Singularly Perturbed Systems

This paper presents a new method for modeling a two-time-scale system in the singularly perturbed form. The method uses an "ordered" real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given in the paper. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form via a transformation into an "ordered" real Schur form, followed by balancing. Second, under some conditions on the "ordered" real Schur decomposition a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, a procedure is given to achieve modeling by permuting the original state variables. The conditions under which this latter procedure works are necessary and sufficient.