Coprime Factor Perturbation in Robust Control for Lightly Damped System

The $\mathrm{H}_{\infty}$ loop shaping method based on coprime factorization is widely used in the design of flexible systems. In the paper $\mathrm{H}_{\infty}$ loop shaping design for lightly damped system shows coprime factor perturbations can be used to represent parameter perturbation in the robust design, but it also reduces the robustness of the design. So coprime factor perturbation is not effective like recognized, its use is limited. The paper detailed analysis of coprime factor perturbation, with a lightly damped system parameter perturbation designed to illustrate the robustness of prime factorization problem occurs in use.