Relations between (H∞) optimal control of a nonlinear system and its linearization

In a previous paper we showed some basic connections between H∞ control of a nonlinear control system and H∞ control of its linearization. A key argument was that the existence and parametrization, at least locally, of the stable invariant manifold of a certain Hamiltonian vector field is determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology we are able to give a quick proof of the fact that a nonlinear optimal control problem is locally solvable if the associated LQ problem is solvable. This was proved before under much stronger conditions