Routh Approximations for Reducing Order of Discrete Systems

Abstract

Routh approximation method is extended to the simplification of z-transfer functions. The procedure includes (1) transformation of the z-transfer function into the w-domain, (2) γ-δ expansion of the w-transfer function, (3) truncation the higher-order terms in the γ-δ expansions, and (4) transformation of the reduced w-transfer function into the z-domain. The reduced model is always stable if the original high-order system is stable. A numerical example is inclinded to illustrate the procedure.