A generalization of Bessel's approximation and its application to model reduction

Abstract

The direct continued-fraction method for model reduction corresponds to the Pode formula. The squared magnitude continued-fraction method for stable reduced models is a modification of the direct method. We naturally think of the counterpart of the squared magnitude continued-fraction method—the tangent phase function. This paper establishes a detailed procedure for the continued-fraction expansion of the tanget phase function. It turns out that the procedure is a generalization of the Bessel filter approximation. Therefore, new light has been shed on the classical filter problem. Two demonstrative examples—a pitch rate control of a supersonic transport aircraft and a pupil reflex system—are included.