The authors consider control systems of the type \[ \dot x= f(x,\sigma(u)),\quad x(0)= x_0,\quad t\geq 0, \] where \(\sigma\) denotes an input nonlinearity -- in many cases saturation -- and present a methodology for designing globally stabilizing nonlinear controllers. An optimal control framework is used which additionally guarantees that the closed-loop system is robustly stable over a class of time-invariant, sector bounded, memoryless nonlinearities. This is accomplished by choosing the controller such that the time derivative of the control Lyapunov function is negative along the closed-loop system trajectories while providing sufficient conditions for the existence of asymptotically stabilizing solutions to the Hamilton-Jacobi-Bellman equation. Solution of the latter is avoided; the controllers are obtained from an inverse optimal control problem. The authors parametrize a family of stabilizing nonlinear controllers that minimize some derived cost functional. The paper concludes with an example for saturation control.