On the structured distance to uncontrollability

This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the μ-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate that the structured distance can differ from the standard, unstructured distance to uncontrollability by an arbitrary amount. It is also shown how systems of higher order and periodic systems can be addressed.