  We consider the problem of global stabilization of an unstable bioreactor
model (e.g. for anaerobic digestion), when the measurements are discrete and in
finite number ("quantized"), with control of the dilution rate. The model is a
differential system with two variables, and the output is the biomass growth.
The measurements define regions in the state space, and they can be perfect or
uncertain (i.e. without or with overlaps). We show that, under appropriate
assumptions, a quantized control may lead to global stabilization: trajectories
have to follow some transitions between the regions, until the final region
where they converge toward the reference equilibrium. On the boundary between
regions, the solutions are defined as a Filippov differential inclusion. If the
assumptions are not fulfilled, sliding modes may appear, and the transition
graphs are not deterministic.
