example.refs.bib

@article{SON2010476,
title = {The structured distance to uncontrollability under multi-perturbations: An approach using multi-valued linear operators},
journal = {Systems \& Control Letters},
volume = {59},
number = {8},
pages = {476-483},
year = {2010},
issn = {0167-6911},
doi = {https://doi.org/10.1016/j.sysconle.2010.06.007},
url = {https://www.sciencedirect.com/science/article/pii/S016769111000071X},
author = {Nguyen Khoa Son and Do Duc Thuan},
keywords = {Linear systems, Distance to uncontrollability, Multi-valued linear operators, Multi-perturbations},
abstract = {In this paper we develop a unifying approach for computing the distance to uncontrollability of linear control systems. By using multi-valued linear operators in representing and estimating the system’s equations and matrices we are able to derive computable formulas of the distance from a controllable linear system to the nearest uncontrollable system under the assumption that the system’s matrices are subjected to structured multi-perturbations and measured by arbitrary operator norms. In the case of spectral norms, the obtained results unify and extend some previous works as well as a recent interesting result in [M. Karrow, D. Kressner, On the structured distance to uncontrollability, Systems Control Lett. 58 (2009) 128–132]. Some illustrating examples are given.}
}