Conservatism of the gap metric

It is shown by way of simple examples that the gap metric may be inappropriate for quantifying the uncertainty for lightly damped systems, e.g., flexible structures such as spacecraft and aircraft. Two plants having otherwise identical transfer functions, except their zeros on the imaginary axis are located slightly apart due to perturbations, are usually considered very close, i.e., their closed loop characteristics under most stabilizing feedbacks are very similar. However, it is demonstrated that, when using the gap to quantify the plant perturbations, the computed gap may be large. Consequently, the stability of the perturbed plant with stabilizing controller designed for the nominal plant cannot be guaranteed via the existing stability theorems using the gap metric