We study control problems for chemostat models with one species, one limiting substrate, and a constant sub-strate input concentration. We allow Haldane growth functions and other growth functions that are not necessarily monotone. The measurement is assumed to be the substrate concentration, which is piecewise constant with a constant delay. Under conditions on the size of the delay and on the largest sampling interval, we solve the problem of asymptotically stabilizing a componentwise positive equilibrium point with the dilution rate as control. We use a new type of Lyapunov approach.