Inserted: 6 sep 2007
Last Updated: 1 aug 2008
Journal: ESAIM Control Optim. Calc. Var.
We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.