Stability Analysis of Polynomially Dependent Systems by Eigenvalue Perturbation

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

4 Scopus Citations
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Author(s)

  • Jie Chen
  • Peilin Fu
  • César-Fernando Méndez-Barrios
  • Silviu-Iulian Niculescu
  • Hongwei Zhang

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number7801025
Pages (from-to)5915-5922
Journal / PublicationIEEE Transactions on Automatic Control
Volume62
Issue number11
Online published25 Oct 2017
Publication statusPublished - Nov 2017

Abstract

In this technical note we present a stability analysis approach for polynomially-dependent one-parameter systems. The approach, which appears to be conceptually appealing and computationally efficient and is referred to as an eigenvalue perturbation approach, seeks to characterize the analytical and asymptotic properties of eigenvalues of matrix-valued functions or operators. The essential problem dwells on the asymptotic behavior of the critical eigenvalues on the imaginary axis, that is, on how the imaginary eigenvalues may vary with respect to the varying parameter. This behavior determines whether the imaginary eigenvalues cross from one half plane into another, and hence plays a critical role in determining the stability of such systems. Our results reveal that the eigenvalue asymptotic behavior can be characterized by solving a simple generalized eigenvalue problem, leading to numerically efficient stability conditions.

Research Area(s)

  • Asymptotic zero behavior, eigenvalue perturbation, matrix pencil, polynomially-dependent systems, stability

Citation Format(s)

Stability Analysis of Polynomially Dependent Systems by Eigenvalue Perturbation. / Chen, Jie; Fu, Peilin; Méndez-Barrios, César-Fernando; Niculescu, Silviu-Iulian; Zhang, Hongwei.

In: IEEE Transactions on Automatic Control, Vol. 62, No. 11, 7801025, 11.2017, p. 5915-5922.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review