Exponential stability of nonlinear infinite-dimensional systems: Application to nonisothermal axial dispersion tubular reactors

Hastir, Anthony;Winkin, Joseph J.;Dochain, Denis
(2020) Automatica — Vol. 121, p. 109201 (2020)

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  • Hastir, AnthonyUniversity of Namur, Department of Mathematics and Namur Institute for Complex Systems (naXys),Belgium
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  • Winkin, Joseph J.University of Namur, Department of Mathematics and Namur Institute for Complex Systems (naXys),Belgium
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  • Dochain, Denisorcid-logoUCLouvain
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Abstract
Exponential stability of equilibria of nonlinear distributed parameter systems is considered. A general framework is set with related assumptions. In particular it is shown how to get local exponential stability of an equilibrium profile for the corresponding nonlinear system based on stability results for the linearized one. For this purpose a weakened concept of Fréchet differentiability is required for the nonlinear semigroup generated by the nonlinear model, with links to Al Jamal and Morris (2018). The theoretical results are applied to a nonisothermal axial dispersion tubular reactor model and are illustrated with numerical simulations.
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Hastir, A., Winkin, J. J., & Dochain, D. (2020). Exponential stability of nonlinear infinite-dimensional systems: Application to nonisothermal axial dispersion tubular reactors. Automatica, 121, 109201. https://doi.org/10.1016/j.automatica.2020.109201 (Original work published 2020)