Computing control Lyapunov functions via a Zubov type algorithm

We present a scheme for the determination of control Lyapunov functions which can be used as a basis for numerical computations. Under the assumption of local asymptotic null-controllability, we define the domain of asymptotic null-controllability. On this setting a control Lyapunov function is defined via an optimal control problem. It is then shown that this function can be characterized as the unique viscosity solution of a partial differential equation which can be interpreted as a generalization of Zubov's equation.