MODEL-REDUCTION USING NEW OPTIMAL ROUTH APPROXIMANT TECHNIQUE

An optimal Routh approximant of a single-input single-output dynamic s ystem is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is det ermined by minimizing a time-response integral-squared-error (ISE) cri terion. In this paper, a new elegant approach is presented for obtaini ng the optimal Routh approximants for linear time-invariant continuous -time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in o rder to obtain the optimal bilinear Routh approximants of linear time- invariant discrete-time systems. The proposed technique is simple in f ormulation and is amenable to practical implementation.