On selecting a low-order model using the dominant mode concept

A technique for selecting a low-order system to approximate a high-order model has been suggested by Davison [2]. A critical component in this technique is the criterion used to select the most appropriate order and modes for the low-order approximation. Criteria have been discussed and analyzed by Mahapatra [5], [6], Rao, Lamba, and Rao [7], and Elrazaz and Sinha [3]. In this note we overcome deficiencies in the criteria that have been proposed and we introduce a new criterion which is rigorously justified. The criterion we suggest is also applicable when eigenvalues of the system are nonreal.