Abstract
This paper derives a method to calculate the Hankel singular values of input time delay systems. The method uses the property that the gramian is an integral operator with a semi-seperable kernel function, and hence is represented as a Volterra operator plus a finite-dimensional operator. The Hankel singular values are obtained by calculating a transcendental equation involving the determinant of the associated finite-dimensional matrix functions. The relation between this result and the result in the literature is explained explicitly, by coordinate transformation. Futhermore, lower and upper bounds on their values are estabilished using the minimax properties of the eigenvalues for a compact and non-negative self-adjoint operator. This result shows that as the length of delay increases, all the Hankel singular values have a monotone increasing property.
