Equivalence of bilinear Routh and Schwarz approximation methods for discrete-time systems

Two methods using the bilinear Routh approximations and Schwarz approximations have been proposed in the literature for the order reduction of discrete-time systems. Both methods yield the reduced models which preserve the stability and first few time-moments of the original ones. Recently, improvements have been made so that the impulse response energies of original models are also retained in the reduced models. In this Letter, it is shown that the former two methods and their improved versions are respectively equivalent to each other