Stabilization of fronts in a reaction - Diffusion system: Application of the Gershgorin theorem

Yelena Smagina; Olga Nekhamkina; Moshe Sheintuch

doi:10.1021/ie001003n

Stabilization of fronts in a reaction - Diffusion system: Application of the Gershgorin theorem

Yelena Smagina^*, Olga Nekhamkina, Moshe Sheintuch

^*Corresponding author for this work

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

20 Scopus citations

Abstract

A formal approach for control design aimed at stabilization of front and pulse patterns in parabolic quasilinear PDE systems using proportional weighted-average feedback regulators and inhomogeneous actuators is suggested and demonstrated. The method capitalizes on the structure of the Jacobian matrix of the system, presented by a finite Fourier series in eigenfunctions. The finite bandwidth of this matrix and the dissipative nature of the parabolic PDE allow for the construction of the finite feedback regulator by direct application of the Gershgorin stability theorem. Whereas this formalism was rigorously proven for polynomial source functions, we expect this approach to apply to other systems as well. The control obtained stabilizes the solutions in a wide range within the bistability domain. The results are compared with those of other control approaches.

Original language	English
Pages (from-to)	2023-2032
Number of pages	10
Journal	Industrial and Engineering Chemistry Research
Volume	41
Issue number	8
DOIs	https://doi.org/10.1021/ie001003n
State	Published - 17 Apr 2002
Externally published	Yes

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title = "Stabilization of fronts in a reaction - Diffusion system: Application of the Gershgorin theorem",

abstract = "A formal approach for control design aimed at stabilization of front and pulse patterns in parabolic quasilinear PDE systems using proportional weighted-average feedback regulators and inhomogeneous actuators is suggested and demonstrated. The method capitalizes on the structure of the Jacobian matrix of the system, presented by a finite Fourier series in eigenfunctions. The finite bandwidth of this matrix and the dissipative nature of the parabolic PDE allow for the construction of the finite feedback regulator by direct application of the Gershgorin stability theorem. Whereas this formalism was rigorously proven for polynomial source functions, we expect this approach to apply to other systems as well. The control obtained stabilizes the solutions in a wide range within the bistability domain. The results are compared with those of other control approaches.",

author = "Yelena Smagina and Olga Nekhamkina and Moshe Sheintuch",

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T1 - Stabilization of fronts in a reaction - Diffusion system

T2 - Application of the Gershgorin theorem

AU - Smagina, Yelena

AU - Nekhamkina, Olga

AU - Sheintuch, Moshe

PY - 2002/4/17

Y1 - 2002/4/17

N2 - A formal approach for control design aimed at stabilization of front and pulse patterns in parabolic quasilinear PDE systems using proportional weighted-average feedback regulators and inhomogeneous actuators is suggested and demonstrated. The method capitalizes on the structure of the Jacobian matrix of the system, presented by a finite Fourier series in eigenfunctions. The finite bandwidth of this matrix and the dissipative nature of the parabolic PDE allow for the construction of the finite feedback regulator by direct application of the Gershgorin stability theorem. Whereas this formalism was rigorously proven for polynomial source functions, we expect this approach to apply to other systems as well. The control obtained stabilizes the solutions in a wide range within the bistability domain. The results are compared with those of other control approaches.

AB - A formal approach for control design aimed at stabilization of front and pulse patterns in parabolic quasilinear PDE systems using proportional weighted-average feedback regulators and inhomogeneous actuators is suggested and demonstrated. The method capitalizes on the structure of the Jacobian matrix of the system, presented by a finite Fourier series in eigenfunctions. The finite bandwidth of this matrix and the dissipative nature of the parabolic PDE allow for the construction of the finite feedback regulator by direct application of the Gershgorin stability theorem. Whereas this formalism was rigorously proven for polynomial source functions, we expect this approach to apply to other systems as well. The control obtained stabilizes the solutions in a wide range within the bistability domain. The results are compared with those of other control approaches.

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DO - 10.1021/ie001003n

M3 - 文章

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VL - 41

SP - 2023

EP - 2032

JO - Industrial and Engineering Chemistry Research

JF - Industrial and Engineering Chemistry Research

IS - 8

ER -

Stabilization of fronts in a reaction - Diffusion system: Application of the Gershgorin theorem

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