Eigenvalue clustering, control energy, and logarithmic capacity

Alex Olshevsky

doi:10.1016/j.sysconle.2016.06.013

Eigenvalue clustering, control energy, and logarithmic capacity

Alex Olshevsky

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Pages (from-to)	45-50
Number of pages	6
Journal	Systems and Control Letters
Volume	96
DOIs	https://doi.org/10.1016/j.sysconle.2016.06.013
State	Published - Oct 1 2016

Keywords

Control energy
Control of large scale systems
Discrete-time
Eigenvalue clustering
Linear systems

ASJC Scopus subject areas

Control and Systems Engineering
General Computer Science
Mechanical Engineering
Electrical and Electronic Engineering

Online availability

10.1016/j.sysconle.2016.06.013

Library availability

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AB - 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.

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KW - Control of large scale systems

KW - Discrete-time

KW - Eigenvalue clustering

KW - Linear systems

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ER -

Eigenvalue clustering, control energy, and logarithmic capacity

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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