A NEW 2-STEP ITERATIVE METHOD FOR OPTIMAL REDUCTION OF LINEAR SISO SYSTEMS

A new two-step iterative procedure is proposed for the optimal reduced -order modeling of linear time-invariant single-input single-output (S ISO) systems. The performance index of optimal reduction is taken to b e a quadratic function of the error between the time responses of the original and reduced models. At each iteration cycle, the numerator dy namics is first determined by solving a set of linear equations, and t he denominator polynomial is then determined by a gradient-based searc h technique. The main features of the proposed procedure are that it s earches the Routh stability parameters rather than the denominator pol ynomial coefficients of the reduced model, and computes the performanc e index and its gradients by a computationally efficient parametric al gorithm. As a consequence, the need of stability monitoring in the ste p of searching optimal denominator polynomial for the reduced model is avoided, and the gradient vector evaluated exactly and efficient for a gradient-based parameter search. Moreover, the constraint of zero, s teady-state response error can be easily handled. Copyright (C) 1996 P ublished by Elsevier Science Ltd