Stability Optimization for Polynomials and Matrices

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The chapter addresses polynomials, for which some remarkable analytical results are available in one special case. It considers the more general case of matrices, focusing on the static output feedback (SOF) problem arising in control of linear dynamical systems. The chapter discusses some spectral radius optimization problems arising in the analysis of the transient behavior of a Markov chain and the design of smooth surfaces using subdivision algorithms. Optimization of roots of polynomials can arise in many contexts, but perhaps the most important application area is feedback control in the frequency domain. As control feedback problems in the frequency domain are a source of applications for polynomial root optimization problems, so control feedback problems in state space are a source of applications for eigenvalue optimization problems. The structure present in a matrix family may lead to local optimizers with active derogatory eigenvalues, even though non-derogatory eigenvalues are the most generic.

Original languageEnglish (US)
Title of host publicationNonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations
PublisherWiley Blackwell
Pages351-375
Number of pages25
ISBN (Print)9781118577608, 9781848214200
DOIs
StatePublished - Dec 31 2013

Fingerprint

Feedback Control
Optimization Problem
Polynomial
Frequency Domain
Optimization
Eigenvalue Optimization
Subdivision Algorithm
Polynomial Roots
Eigenvalue
Static Output Feedback
Linear Dynamical Systems
Transient Behavior
Smooth surface
Spectral Radius
Eigenvalue Problem
Markov chain
State Space
Roots
Context
Design

Keywords

  • Eigenvalues
  • Markov chain
  • Matrices
  • Polynomials
  • Spectral radius
  • Stability optimization
  • Static output feedback (SOF)

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Overton, M. L. (2013). Stability Optimization for Polynomials and Matrices. In Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations (pp. 351-375). Wiley Blackwell. https://doi.org/10.1002/9781118577608.ch16

Stability Optimization for Polynomials and Matrices. / Overton, Michael L.

Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations. Wiley Blackwell, 2013. p. 351-375.

Research output: Chapter in Book/Report/Conference proceedingChapter

Overton, ML 2013, Stability Optimization for Polynomials and Matrices. in Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations. Wiley Blackwell, pp. 351-375. https://doi.org/10.1002/9781118577608.ch16
Overton ML. Stability Optimization for Polynomials and Matrices. In Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations. Wiley Blackwell. 2013. p. 351-375 https://doi.org/10.1002/9781118577608.ch16
Overton, Michael L. / Stability Optimization for Polynomials and Matrices. Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations. Wiley Blackwell, 2013. pp. 351-375
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