We conduct a linear stability analysis of Rayleigh-Bénard convection in an infinite horizontal layer with active control of the lower boundary heat flux. A simple linear proportional control loop uses a shadowgraph of the convection pattern to actively distribute the constant-mean lower boundary heat flux while the upper boundary is kept at a constant temperature. We find it possible to shift the convection threshold by a factor of approximately 3. This is a companion paper to our recent experimental work. © 1997, American Institute of Physics. All rights reserved.