Realization of Cauer third form by integrators

The realization of Cauer third form of continued fraction expansion (CFE) by both integrators and differentiators is restricted to even-order systems. In this paper we present a new realization form which involves integrators only and is applicable to both odd- and even-order systems. A new similarity transformation matrix is derived to transform a state-space model in its phase-variable canonical form to that in the new Cauer third CFE canonical form. This transformation matrix can be used to construct an approximate aggregation matrix which relates the states of a high-order system and its reduced-order model obtained by the method of the new Cauer third form.