A new two-step iterative method for optimal reduction of linear SISO systems
This paper discusses the model reduction problem of SISO systems. A strictly proper rational transfer function \(G_n\) of degree \(n\) is approximated by a strictly proper rational transfer function \(G_m\) of lower degree \(m<n\). The approximation criterion is to minimise \(\int_0^\infty e(t)^2dt\) where \(e(t)\) is the response of the system with transfer function \(G_n-G_m\) to an input with Laplace transform \(R(s)=s^{-l}\) where \(l=0\) or 1. The classical free parameters of the problem (the coefficients of the numerator and denominator of \(G_m\)) are replaced by the Routh stability parameters of the denominator and the coefficients of the numerator. Then stability of the approximant is guaranteed if these Routh parameters are subject to a simple positivity constraint. The solution of this constrained optimization problem is based on a gradient method. Explicit expressions for this gradient are derived. The iteration alternates between an update of the Routh parameters and an update of the numerator coefficients.
scientific article; zbMATH DE number 1060097
scientific article