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 between the two have not been established. We address the problem in two ways, and show that it is possible to establish an explicit connection using a method that is very reminiscent of the way singular values are usually defined for compact linear operators