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Stability and Instability Intervals of Polynomially Dependent Systems : An Matrix Pencil Analysis

Abstract : In this paper 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 functionsor 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.
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Conference papers
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https://hal-centralesupelec.archives-ouvertes.fr/hal-02276316
Contributor : Delphine Le Piolet <>
Submitted on : Monday, September 2, 2019 - 3:04:07 PM
Last modification on : Wednesday, September 16, 2020 - 5:20:41 PM

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  • HAL Id : hal-02276316, version 1

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Jie Chen, Peilin Fu, César Fernando Méndez Barrios, Silviu-Iulian Niculescu, Hongwei Zhang. Stability and Instability Intervals of Polynomially Dependent Systems : An Matrix Pencil Analysis. ACC 2017 - American Control Conference, May 2017, Seattle, WA, United States. ⟨hal-02276316⟩

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