Distance Measures for Strong Observability and Strong Detectability of Systems with Direct Feedthrough

This letter presents distance measures for strong observability and strong detectability of linear, time-invariant systems with direct feedthrough. In contrast to standard binary criteria, the proposed measures allow to quantify these properties numerically. An optimization based approach for calculating these measures is derived. Meaningful conditions for such measures are introduced and the properties of the proposed measures regarding these conditions are analyzed. In order to demonstrate their usefulness, the measures are applied to optimal sensor placement for reconstruction of unknown forces on a mechanical structure.