Multiplicative approximation of multivariable systems using Hankel norm criterion

Abstract

Control system design specifications are commonly given in terms of log-magnitude quantities (dB). This induces a multiplicative or relative error criterion for plant model reduction. Techniques from the theory of additive Hankel norm approximation and spectral factorization are synthesised to produce a multiplicative approximant of a possibly unstable or nonsquare plant. It is shown that the reduced-order model preserves the right half plane poles and zeros of the original system. Explicit state-space formulae are provided for the construction of the reduced order model and its error properties discussed.