Basic procedure for model comparison using the gap metric

This paper introduces an angular measure called the ‘gap metric’ as a tool for comparing linear models which are not necessarily stable or proper. It is shown that the gap is superior to the usual norm distance metric, particularly when the models have high gain or open right half-plane poles and zeros. A BASIC microcomputer procedure is presented to aid in interactive design work using the gap. Examples are included which demonstrate that the gap is an exact measure in certain situations and may be a valuable approximation in others.