A survey of balancing methods for model reduction

Balancing is one of the most efficient and most commonly used methods for model reduction. In this note, we present a survey of several balancing related model reduction schemes. Also we introduce a multiplicative error bound and propose a new reduction method with an absolute error bound for positive real balancing. In addition, a frequency weighted balancing technique with guaranteed stability and a simple bound on the H∞ norm of the error system, is presented.