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 journalArticlepeer-review

20 Scopus citations


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 languageEnglish
Pages (from-to)2023-2032
Number of pages10
JournalIndustrial and Engineering Chemistry Research
Issue number8
StatePublished - 17 Apr 2002
Externally publishedYes


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