"We present a method for stabilization of a class of nonlinear systems. The notion of stability preservation is exploited to prove that a transformation allows to find a stabilizer. The nonlinear systems have uncontrollable linearized system. From this fact, we propose a method that departs from a controllable linearized system to a linear transformation. The linear transformation allows to take the uncontrolled system preserving the stability properties of the controlled one. Thus, the resulting controller is able to stabilize biomedical systems. Type I diabetes mellitus and HIV-I diseases are used to show the potential of method. Numerical simulations for this case illustrate the performance of closed loop approach."