Singular perturbation approximation of bounded real balanced and stochastically balanced transfer matrices

In this work, model reduction of Bounded Real and Positive Real transfer matrices is considered. Singular perturbation approximations of bounded real and stochastically balanced systems are proposed and their properties are shown. In particular it is shown that the reduced-order models remain bounded real and positive real respectively and bounds on the approximation errors are obtained. Moreover, several considerations concerning the relative/multiplicative error reduction method are reported. Three numerical examples, showing the suitability of the proposed method, conclude the paper.