Abstract:The problems of feedback control and stability regions estimation for a class of the continuous differential equation models of the interaction dynamics of HIV-1 and CD4 and CD8 lymphocytes in the human body is investigated. First, the control law is derived such that in the closed-loop system, the states that represent CD4, CD8 and viral load, are regulated to a specified equilibrium point in the state space. The stabilizing controller is analogous to require only finite and little therapeutic drug regimen. Furthermore, the exact information about the equilibrium may not be available, although the CD4 and CD8 populations in a human have a typical range of equilibrium values. We will propose a linear adaptation law and examine the conditions under which it achieves the stabilization of the unknown equilibrium. Finally, the approach to estimate stability regions of HIV-1 controlled systems using the concepts of vector norms, comparison systems and overvaluing systems is developed.