  In this paper, we investigate the perturbation analysis of $A_{T,S}^{(2)}$
when $T,\,S$ and $A$ have some small perturbations on Hilbert spaces. We
present the conditions that make the perturbation of $A_{T,S}^{(2)}$ is stable.
The explicit representation for the perturbation of $A_{T,S}^{(2)}$ and the
perturbation bounds are also obtained.
