Hankel singular value functions from Schmidt pairs for nonlinear input–output systems

Hankel singular value functions from Schmidt pairs for nonlinear input-output systems

This paper presents three results in singular value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel singular value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known...

On Singular Value Functions and Hankel Operators for Nonlinear Systems

In linear system theory, the Hankel singular values are often computed in a state space setting using the product of Gramian matrices. They are known, however, to be intrinsically dependent only on the input-output map and not on any choice of state space coordinates. In the nonlinear case, there are well defined notions of singular value functions and a Hankel operator, but the connections bet...

On Adjoints and Singular Value Functions for Nonlinear Systems

Jacquelien M.A. Scherpen ∗ Fac. ITS, Dept. of Electrical Eng., Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands. [email protected] Kenji Fujimoto∗,∗∗ ∗∗ Department of Systems Science Graduate School of Informatics, Kyoto University, Uji, Kyoto 611-0011 Japan. [email protected], [email protected] W. Steven Gray Department of Electrical and ...

A Fast Singular Value Algorithm for Hankel Matri esFranklin

Hamiltonian Extensions, Hilbert Adjoints and Singular Value Functions for Nonlinear Systems

This paper 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 Gâteaux 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 ...