Algorithm for biased continued-fraction expansions of z-transfer functions

A new algorithm is presented for obtaining the biased continued-fraction expansion (BCFE) of Shamash directly from the state-space model of a discrete-time system, without having to determine the corresponding z-transfer function. The algorithm gives a clear indication that system reduction by BCFE is equivalent to matching a set of Markov parameters and modified time moments. A numerical example is given to illustrate the algorithm.