  In this paper, the perturbation problems of $A_{T,S}^{(2)}$ are considered.
By virtue of the gap between subspaces, we derive the conditions that make the
perturbation of $A_{T,S}^{(2)}$ is stable when $T,S$ and $A$ have suitable
perturbations. At the same time, the explicit formulas for perturbation of
$A_{T,S}^{(2)}$ and new results on perturbation bounds are obtained.
