he positivity and linearization of a class of nonlinear continuous-time system by nonlinear state feedbacks are addressed. Necessary and sufficient conditions for the positivity of the class of nonlinear systems are established. A method for linearization of nonlinear systems by nonlinear state feedbacks is presented. It is shown that by a suitable choice of the state feedback, it is possible to obtain an asymptotically stable and controllable linear system. when the closed-loop system is positive, it is unstable. Center manifold theory plays an important role in the study of the stability of dynamical systems when the equilibrium point is not hyperbolic. The center manifold is an invariant manifold of the differential equation which is tangent at the equilibrium point to the eigeace of the neutrally stable eigenvalues.
