Eigenvalue Clustering, Control Energy, and Logarithmic Capacity
arXiv:1511.0020521 citationsh-index: 36
Originality Synthesis-oriented
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Provides theoretical bounds linking eigenvalue distribution to control effort, relevant for control theory and system design.
The paper proves that eigenvalue clustering in a matrix forces high control energy in discrete-time linear systems, with one bound depending on the logarithmic capacity of the region.
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.