Optimizing the Kreiss constant

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.