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

In a previous work (1991), the author 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 are determined by the Hamiltonian matrix corresponding to the linearized problem. Using the same methodology, the author gives 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 by D.L. Lukes (1969) under much stronger conditions