The stability of a four-dimensional nonlinear model of a wastewater treatment process (proposed by Bernard, Hadj-Sadok, Dochain, Genovesi and Steyer in 2001) is studied. A feedback
control law, depending only on on-line measurable quantities, is proposed. This feedback law
stabilizes asymptotically the closed-loop system towards a previously chosen operating point. In
order to prove that the closed-loop system is asymptotically stable, two Lyapunov-like functions
are constructed explicitly. A numerical extremum seeking algorithm is then applied to stabilize
the dynamics towards an equilibrium point corresponding to the maximum methane output flow
rate. The robustness of the feedback is demonstrated by involving uncertainties in the growth
rate model functions. Computer simulations are reported to illustrate the theoretical results.