Late-phasing homogeneous charge compression ignition operating conditions have the potential to expand the useful operating range of homogeneous charge compression ignition in internal combustion engines. However, significant combustion instabilities can occur at late-phasing operating conditions. Combustion phasing and work output variations at these conditions are characterized by a pattern in which the combustion phasing alternates between being earlier than the desired timing and later than the desired timing. This characteristic can be traced to a negative eigenvalue in a simplified, discrete-time analytical model of homogeneous charge compression ignition dynamics. The model forms the basis for the design of a simple controller that is shown to reduce combustion timing variations in simulation. Experimental results illustrate the controller successfully reduces the cyclic variations in combustion by altering the exhaust valve timing, resulting in stable combustion and an expanded operating range.