A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of eta -dimensional closed balls B-r(eta) (p), which are defined by means of a p-norm and a radius vector parameter r. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c-parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations(required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.