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1 Systems Science

1 2004

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Reduction of linear discrete time systems in frequency domain using continued fraction expansions

Prasad R., Devi S.

Systems Science

2004

Vol. 30, no 1

65-76

The continued fraction expansions (CFE) approach coupled with several powerful stable reduction methods is proposed for the reduction of high order z-transfer functions. These methods include the advantages of stability preservation methods (SPM), such as Routh approximation, Routh Hurwitz array and stability equation method etc., with those of the method based on continued fraction expansions. The high order z-transfer functions are transformed in w-domain using bilinear transformation and the denominator of the reduced models are found in w-domain. The numerators of reduced order models are determined by matching the quotients of continued fraction expansions in w-domain. Finally, the reduced z-transfer functions are determined using reverse bilinear transformation. In this paper, combined features of SPM and CFE have been utilised to reduce the linear discrete time systems. To match the initial value of the original step response the bilinear transformation is applied in the high order z transfer function in such a way that the numerator and denominator polynomials of original system are separately expressed in w domain. And, to remove any steady error between the system and model responses, steady state values of original, and reduced systems are matched. The method proposed preserves the time domain and frequency domain characteristics and gives stable models for stable systems. An example illustrates the method.