Hankel Singular Values and Vectors of a Class of Infinite-Dimensional Systems: Exact Hamiltonian Formulas for Control and Approximation Problems

Abstract.

This paper derives exact formulas for singular values and vectors of Hankel operators whose symbol is a product of a single-input single-output inner function and a multi-input multi-output rational function. This class of Hankel operators arises from the sensitivity minimization H ^∞ control problem with a rational weight function and the approximation problem of transfer functions having rational outer parts. It is shown that there is a Hamiltonian transcendental equation characterizing singular values which leads to a matrix function formula for singular vectors.