A multipoint continued-fraction expansion for linear system reduction

This note presents a multipoint continued-fraction expansion (MCFE) to obtain reduced models for linear time-invariant systems. Algorithms for the expansion and inversion of the MCFE are outlined. A realization for the MCFE of a transfer function is suggested, and the corresponding MCFE canonical state-space model is established. A new similarity transformation matrix is constructed to transform a state-space model in the phase-variable canonical form to one in the MCFE canonical form. The attractive feature of the present MCFE is that it is general in form and the resulting reduced models approximate well the original system in both the frequency and time responses.