Eigenvalue clustering, control energy, and logarithmic capacity

Alex Olshevsky

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Pages (from-to)45-50
Number of pages6
JournalSystems and Control Letters
StatePublished - Oct 1 2016


  • 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


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