Boundary feedback stabilization of the Schlögl system

Journal article
(Original article)


Publication Details

Author(s): Gugat M, Tröltzsch F
Journal: Automatica
Publisher: Elsevier
Publication year: 2015
Volume: 51
Pages range: 192-199
ISSN: 0005-1098


Abstract


The Schlögl system is governed by a nonlinear reaction-diffusion partial differential equation with a cubic nonlinearity that determines three constant equilibrium states. It is a classical example of a chemical reaction system that is bistable. The constant equilibrium that is enclosed by the other two constant equilibrium points is unstable. In this paper, Robin boundary feedback laws are presented that stabilize the system in a given stationary state or more generally in a given time-dependent desired system orbit. The exponential stability of the closed loop system with respect to the L2-norm is proved. In particular, it is shown that with the boundary feedback law the unstable constant equilibrium point can be stabilized.



FAU Authors / FAU Editors

Gugat, Martin apl. Prof. Dr.
Lehrstuhl für Angewandte Mathematik


External institutions with authors

Technische Universität Berlin


How to cite

APA:
Gugat, M., & Tröltzsch, F. (2015). Boundary feedback stabilization of the Schlögl system. Automatica, 51, 192-199. https://dx.doi.org/10.1016/j.automatica.2014.10.106

MLA:
Gugat, Martin, and Fredi Tröltzsch. "Boundary feedback stabilization of the Schlögl system." Automatica 51 (2015): 192-199.

BibTeX: 

Last updated on 2018-07-08 at 10:23