An improved algorithm for partial fraction expansion based frequency weighted balanced truncation

Abstract

In this paper, we present an improvement to frequency weighted balanced truncation technique based on well-known partial fraction expansion. The method yields stable reduced-order model for double-sided weightings. A numerical example and comparison with other well-known techniques shows that a significant approximation error reduction can be achieved using this improvement.

Reduced-Order Reference Models for Adaptive Control of Space Structures

“…By applying input and output filters to the model, inputs and outputs at some frequencies can be made more controllable/observable than others to highlight the ranges of operating frequencies; the controllability and observability gramians then take the effect of the filters into account, altering balancing transformation accordingly. Some ongoing work on this approach has been aimed at reducing the approximation error, with recent gains apparently being made by some, such as Muda et al in [19].…”