Abstract: In this paper, we firstly investigate the input-to-state stabilization of affine systems whose unforced dynamics are critically stable. Using the hypothesis of zerostate detectability we obtain a result that weakens the general precondition that unforced dynamics are globally asymptotically stable. We then apply the passivity theory to studies of disturbance attenuation, and put forward concise conditions guaranteeing negative output feedback to solve disturbance attenuation problems. In our analysis Legendre-Fenchel transformation is used.