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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