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Comparative study of model reduction schemes - application to the digital filters synthesis

We present a comparative study of recent methods for simplifying large-scale systems via low-order models, such as the Schur, the balanced realizations, the balanced gains, and the optimal aggregation approaches that we group under the nomination of internal projections, defining a new class of model reduction scheme. These approaches use the state-space representation and develop algorithms in order to obtain a new low-order state-representation. Through an illustrative example, where all methods are applied for the simplification of a given digital prototype Cauer filter, a comparative performance study is done.