# Mixed control of vibrational systems

## TL;DR

This paper introduces new $H_2$ norm-based performance measures for vibrational systems, demonstrating their advantages over standard measures through theoretical analysis and numerical experiments to optimize damping strategies.

## Contribution

It proposes novel $H_2$ norm-based performance measures for vibrational systems and evaluates their effectiveness in optimizing damping configurations.

## Key findings

- New measures outperform standard ones in certain scenarios
- Optimal damping positions vary with new measures
- Numerical experiments validate theoretical advantages

## Abstract

We consider new performance measures for vibrational systems based on the $H_2$ norm of linear time invariant systems. New measures will be used as an optimization criterion for the optimal damping of vibrational systems. We consider both theoretical and concrete cases in order to show how new measures stack up against the standard measures. The quality and advantages of new measures as well as the behaviour of optimal damping positions and corresponding damping viscosities are illustrated in numerical experiments.