Eigenvalue Clustering, Control Energy, and Logarithmic Capacity
Optimization and Control
2016-04-26 v3 Systems and Control
Abstract
We prove two bounds showing that if the eigenvalues of a matrix are clustered in a region of the complex plane then the corresponding discrete-time linear system requires significant energy to control. A curious feature of one of our bounds is that the dependence on the region is via its logarithmic capacity, which is a measure of how well a unit of mass may be spread out over the region to minimize a logarithmic potential.
Cite
@article{arxiv.1511.00205,
title = {Eigenvalue Clustering, Control Energy, and Logarithmic Capacity},
author = {Alex Olshevsky},
journal= {arXiv preprint arXiv:1511.00205},
year = {2016}
}