Boundary feedback stabilization of the Schlögl system
Gugat M, Tröltzsch F (2015)
Publication Type: Journal article, Original article
Publication year: 2015
Journal
Publisher: Elsevier
Book Volume: 51
Pages Range: 192-199
DOI: 10.1016/j.automatica.2014.10.106
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.
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Germany (DE)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.
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