Using mathematical models that show the host-pathogen interaction of the immune system with the HIV virus, this paper identifies the extent to which the stages in the progression of HIV AIDS are controllable, given that the available treatment strategies are constrained. These constraints are the imperfect inhibition of the replication of the virus by the available drugs, undesirable side effects and the ability of the virus to become resistant to drugs. This paper shows how controllability analysis can be applied to HIV AIDS models to identify stages where therapy initiation can benefit the patient more.