Robustness of H_∞ loop shaping design

The uncertainty of the system in the loop shaping design is represented by coprime factor perturbations. These coprime factor perturbations are analyzed in detail in the paper, and it is pointed out that the lightly damped resonant poles of the plant can increase the norm of the coprime factor perturbation and greatly reduce the size of allowable perturbation. Thus, the robustness of the system is really lost. This means that the H_∞ loop shaping design may not be a robust design as expected. An example with parameter perturbations is also illustrated in the paper.