Optimizing the Kreiss constant

TL;DR

This paper introduces an efficient method to compute the Kreiss constant of stable matrices and demonstrates how feedback can be used to reduce this constant, thereby diminishing system transients.

Contribution

It provides a novel computational approach for the Kreiss constant and shows how feedback can effectively lower it to improve system transient response.

Findings

Efficient computation method for the Kreiss constant.

Feedback control can significantly reduce the Kreiss constant.

Potential reduction in system transients through feedback.

Abstract

The Kreiss constant $K(A)$ of a stable matrix $A$ conveys information about the transient behavior of system trajectories in response to initial conditions. We present an efficient way to compute the Kreiss constant $K(A)$, and we show how feedback can be employed to make the Kreiss constant $K(A_{cl})$ in closed loop significantly smaller. This is expected to reduce transients in the closed loop trajectories. The proposed approached is compared to potential competing techniques.