Routh type approximation for discrete system

A method of reduction for a discrete system is presented. The denominator of the reduced model is directly obtained in z-domain from the denominator of the higher-order system. The denominator of the reduced model is directly obtained from a Routh-type table. The numerator of the reduced model is obtained either by matching the discrete time moments or by minimizing the step response error constructed in discrete time domain and computed in z-domain. The stability of the reduced model is guaranteed if the higher-order system is stable. A numerical example is examined which involves the determination of a second-order reduced model for a fourth-order digital filter.<>