Hamiltonian extensions, Hilbert adjoints and singular value functions for nonlinear systems

Studies previously developed nonlinear Hilbert adjoint operator theory from a variational point of view and provides a formal justification for the use of Hamiltonian extensions via Gateaux differentials. The primary motivation is its use in characterizing singular values of nonlinear operators, and in particular, the Hankel operator and its relationship to the state space notion of nonlinear balanced realizations.