Refined Schur Method for Robust Pole Assignment with Repeated Poles

TL;DR

This paper introduces a refined Schur method for robust pole assignment that effectively handles repeated poles, overcoming limitations of existing methods when poles are close or multiple.

Contribution

The paper proposes a novel refined Schur method capable of assigning repeated poles and functioning when traditional methods fail due to pole multiplicity.

Findings

Successfully handles repeated poles in robust pole assignment.

Maintains robustness even with high multiplicity of poles.

Outperforms existing methods in challenging pole placement scenarios.

Abstract

Schur-type methods in \cite{Chu2} and \cite{GCQX} solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure of robustness. They work well generally when all poles to be assigned are simple. However, when some poles are close or even repeated, the eigenvalues of the computed closed-loop system matrix might be inaccurate. In this paper, we present a refined Schur method, which is able to deal with the case when some or all of the poles to be assigned are repeated. More importantly, the refined Schur method can still be applied when \verb|place| \cite{KNV} and \verb|robpole| \cite{Tits} fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom.