IEEE Transactions on Automatic Control, Vol.54, No.3, 641-646, 2009
On Hankel Singular Values and Reflected Zeros of Linear Dynamical Systems
This note discusses a relationship between the Hankel singular values and reflected zeros of linear systems. Our main result proves that the Henkel singular values or a linear continuous-time system increase (decrease) pointwise when one or more zeros of the transfer function are reflected with respect to the Imaginary axis, that Is, move from the left-(right)half to the right-(left-)hair of the complex plane. We also derive a similar result for linear discrete-time systems.
Keywords:Hankel singular values;linear continuous-time system;linear discrete-time system;reflected zeros