Eigenvalue Clustering, Control Energy, and Logarithmic Capacity

Alex Olshevsky

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Eigenvalue Clustering, Control Energy, and Logarithmic Capacity

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arxiv 1511.00205 v3 pith:F3F5DHTF submitted 2015-11-01 math.OC cs.SYeess.SY

Eigenvalue Clustering, Control Energy, and Logarithmic Capacity

Alex Olshevsky This is my paper

classification math.OC cs.SYeess.SY

keywords logarithmicregionboundscapacitycontrolenergyclusteredclustering

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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.

Eigenvalue Clustering, Control Energy, and Logarithmic Capacity

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