The value function for the Linear-Quadratic Regulator with conical control constraints

The infinite-horizon continuous-time linear-quadratic regulator problem with conical control constraints is considered. Properties of the optimal value function are studied and illustrated: characterization as a solution to a stationary Hamilton-Jacobi equation; convex conjugacy with a dual value function; approximation via smooth value functions for perturbed problems; differentiability; and utility for stabilizing feedback design.