Hankel Singular Values of Flexible Structures in Discrete Time

Approximate analytical expressions for controllability and observability grammian matrices and Hankel singular values of discrete LTI flexible structures are derived. The diagonal dominance property of the discrete grammians is shown which results in the invariance of the principal directions. The approximate discrete Hankel singular values converge to the continuous formula with increased sampling rate while the controllability and observability grammians go to zero and infinity respectively. The approximate formula are accurate up to frequencies close to the Nyquist.