A novel iterative method to approximate structured singular values

TL;DR

This paper introduces a new iterative approach combining Newton's method and gradient systems to approximate structured singular values, enhancing stability analysis in uncertain control systems.

Contribution

It presents a novel iterative method with an inner-outer scheme for more accurate structured singular value approximation, improving upon existing techniques.

Findings

The method effectively approximates structured singular values.

Numerical results show competitive performance with Matlab's mussv.

The approach offers insights into stability analysis of uncertain systems.

Abstract

A novel method for approximating structured singular values (also known as mu-values) is proposed and investigated. These quantities constitute an important tool in the stability analysis of uncertain linear control systems as well as in structured eigenvalue perturbation theory. Our approach consists of an inner-outer iteration. In the outer iteration, a Newton method is used to adjust the perturbation level. The inner iteration solves a gradient system associated with an optimization problem on the manifold induced by the structure. Numerical results and comparison with the well-known Matlab function mussv, implemented in the Matlab Control Toolbox, illustrate the behavior of the method.