Reduced‐order modelling of linear discrete‐time systems using cauer third continued‐fraction method

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Abstract
In this paper a generalization of the Cauer third continued‐fraction expansion (CFE) is introduced for the reduced‐order modelling of linear time‐invariant discrete‐time systems. First, a new algorithm is presented for obtaining the Cauer third continued‐fraction expansion about z=1 and z=8 of the z‐transfer function of a discrete‐time system from its time‐moments and Markov parameters. Next, a realization of the Cauer third continued‐fraction expansion about z=1 and z=8, and the corresponding CFE canonical state‐space model are derived. Finally, an approximate aggregation matrix is constructed for relating the state‐vector of the reduced‐order CFE canonical state‐space model to that of the original system. An example is included to illustrate the use of the method.