Hamiltonian realizations of
nonlinear adjoint operators
K. Fujimoto,
J.M.A. Scherpen,
W.S. Gray,
Automatica , Vol. 38, 10 (2002) 1769-1775.
Abstract:
This paper addresses the issue of state-space realizations for
nonlinear adjoint operators.
In particular, the relationships between nonlinear Hilbert adjoint
operators,
Hamiltonian extensions and port-controlled Hamiltonian systems are
established.
Then, characterizations of the
controllability, observability and Hankel operators,
are derived from this analysis. The state-space realizations of such
operatorsprovide new insights to nonlinear control systems theory.
Finally, a duality between the controllability and
observability functions will be proven.