A new two-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 (SISO) systems. The performance index of optimal reduction is taken to be a quadratic function of the error between the time responses of the original and reduced models. At each iteration cycle, the numerator dynamics is first determined by solving a set of linear equations, and the denominator polynomial is then determined by a gradient-based search technique. The main features of the proposed procedure are that it searches the Routh stability parameters rather than the denominator polynomial coefficients of the reduced model, and computes the performance index and its gradients by a computationally efficient parametric algorithm. As a consequence, the need of stability monitoring in the step of searching optimal denominator polynomial for the reduced model is avoided, and the gradient vector evaluated exactly and efficiently for a gradient-based parameter search. Moreover, the constraint of zero steady-state response error can be easily handled.