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In this dissertation, the improved methods for some commonly used model reduction methods: (1) Pad''e approximation; (2) Routh approximation; (3) model reduction using balanced reduction, are proposed. At first, the multifrequency Pad''e approximation of s transfer functions is performed via the Jordan-type continued-fraction expansion. An efficient algorithm that requires no complex algebra is derived for expanding a transfer function into a Jordan continued fraction about abitrary points s=.plmin. j wi on the imaginary axis of the s- plane. Also derived is a forward inversion algorithm for inverting a multifrequency Jordan continued-fraction expansion into a rational form. The presented algorithms are amenable for obtaining a family of frequency-response matched models of different orders for a high-order transfer function via a single set of computation. With the successful application on the continuous systems, the order reduction problem of z-transfer .......................
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