A Modified Schur Method for Robust Pole Assignment in State Feedback Control

TL;DR

This paper introduces a modified Schur method for robust pole assignment in state feedback control, improving efficiency and robustness when assigning complex conjugate poles, with better results and lower computational costs.

Contribution

It presents a novel modification to the existing SCHUR method, enabling real Schur form production for complex poles and enhancing robustness and efficiency.

Findings

Produces better or comparable results to existing algorithms

Reduces computational costs significantly

Handles complex conjugate poles effectively

Abstract

Recently, a \textbf{SCHUR} method was proposed in \cite{Chu2} to solve the robust pole assignment problem in state feedback control. It takes the departure from normality of the closed-loop system matrix $A_c$ as the measure of robustness, and intends to minimize it via the real Schur form of $A_c$. The \textbf{SCHUR} method works well for real poles, but when complex conjugate poles are involved, it does not produce the real Schur form of $A_c$ and can be problematic. In this paper, we put forward a modified Schur method, which improves the efficiency of \textbf{SCHUR} when complex conjugate poles are to be assigned. Besides producing the real Schur form of $A_c$, our approach also leads to a relatively small departure from normality of $A_c$. Numerical examples show that our modified method produces better or at least comparable results than both \textbf{place} and \textbf{robpole} algorithms, with much less computational costs.