This paper is concerned with stabilization of non-affine-in-control nonlinear systems, a problem which usually leads to algebraic loops usually broken via dynamical controllers. Conditions in the form of linear matrix inequalities for stabilization of such systems are found by introducing a novel dynamical control scheme based on an exact convex representation of the system nonlinearities. Examples, both physical and numerical, illustrate the proposed methodology as it solves a larger family of stabilization problems.