Constrained optimal Padé model reduction
A frequency-domain multipoint Padé approximation method is given that produces optimal reduced order models, in the least integral square error sense, which are constrained to match the initial time response values of the full and reduced systems for impulse or step inputs. It is seen to overcome a perceived drawback of the unconstrained optimal models, i.e., that they do not guarantee a proper rational reduced order transfer function for a step input. The method is easy to implement when compared to existing constrained optimal methods, and consists of solving only linear sets of equations in an iterative process. It is also seen to be a natural extension of an existing optimal method. Numerical examples are given to illustrate its application.