A spectral condition for asymptotic controllability and stabilization at singular points

We present a spectral condition for the exponential stabilization of nonlinear control systems with constrained control range at singular points. The spectral approach in particular allows us to formulate an equivalence result between exponential null controllability and exponential stabilization by means of a discrete feedback law. The key tool used is a discounted optimal control problem for the corresponding projected semilinear system, which also admits a numerical solution