System reduction by Cauer continued-fraction expansion about s=0 and s=a alternately

Abstract

A new algorithm to obtain the Cauer continued-fraction expansion (CFE) about the origin and about a general point from the time-moments and weighted time-moments of the impulse response of a linear time-invariant system is presented. Also presented is a systematic approach to deriving a similarity transformation matrix that transforms a general state-space model to a state-space model corresponding to the Cauer CFE about s = 0 and s = a alternately. The transformation matrix enables an approximate relationship to be established to relate the state vector of the original system and that of the reduced model obtained by the CFE about s = 0 and s = a alternately. The step of transformation to phase variable canonical form is thus eliminated.