TY - JOUR
T1 - Exponential stability of nonlinear infinite-dimensional systems
T2 - Application to nonisothermal axial dispersion tubular reactors
AU - HASTIR, Anthony
AU - Winkin, Joseph J.
AU - Dochain, Denis
N1 - Funding Information:
This research was conducted with the financial support of F.R.S-FNRS . Anthony Hastir is a FNRS Research Fellow under the grant FC 29535 . The scientific responsibility rests with its authors. The first author would like to sincerely thank François Lamoline for his thorough reading of the paper and his insightful comments. He would also like to thank Professor Hans Zwart for helpful discussions and comments about the paper.
Funding Information:
This research was conducted with the financial support of F.R.S-FNRS. Anthony Hastir is a FNRS Research Fellow under the grant FC 29535. The scientific responsibility rests with its authors. The first author would like to sincerely thank Fran?ois Lamoline for his thorough reading of the paper and his insightful comments. He would also like to thank Professor Hans Zwart for helpful discussions and comments about the paper.
Publisher Copyright:
© 2020 Elsevier Ltd
PY - 2020/11
Y1 - 2020/11
N2 - 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.
AB - 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.
KW - Bistability
KW - Equilibrium profiles
KW - Fréchet/Gâteaux derivatives
KW - Nonisothermal axial dispersion tubular reactor
KW - Nonlinear distributed parameter systems
UR - http://www.scopus.com/inward/record.url?scp=85089549693&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2020.109201
DO - 10.1016/j.automatica.2020.109201
M3 - Article
AN - SCOPUS:85089549693
SN - 0005-1098
VL - 121
JO - Automatica
JF - Automatica
M1 - 109201
ER -