Hankel-Norm Approximation of Large-Scale Descriptor Systems

TL;DR

This paper extends Hankel-norm approximation techniques to large-scale continuous-time descriptor systems, introducing efficient algorithms that improve stability, sparsity handling, and computational efficiency for model reduction.

Contribution

It develops a generalized, efficient algorithm for Hankel-norm approximation of large-scale descriptor systems, including stable and sparse system adaptations.

Findings

Algorithm effectively approximates large-scale systems

Enhanced stability and sparsity handling demonstrated

Numerical examples validate approximation quality

Abstract

The Hankel-norm approximation is a model reduction method which provides the best approximation in the Hankel semi-norm. In this paper the computation of the optimal Hankel-norm approximation is generalized to the case of linear time-invariant continuous-time descriptor systems. An efficient algorithm is developed by refining the generalized balanced truncation square root method. For a wide practical usage, adaptations of the introduced algorithm towards stable computations and sparse systems are made as well as an approach for a projection-free algorithm. To show the approximation behavior of the introduced method, numerical examples are presented.