The problem of robust stabilization is considered for a class of nonlinear interconnected systems, which consist of linear subsystems coupled by nonlinear interconnections that are unknown and quadratically bounded. A decentralized dynamic output feedback based linear controller is proposed, where the feedback gain matrices of local controllers are obtained by solving an optimization problem subject to linear matrix inequalities. Local sliding mode observers are employed to asymptotically estimate the subsystems' states and, at the same time, to reconstruct the unknown nonlinear interconnections. The closed-loop system driven by the proposed decentralized dynamic output feedback controller is guaranteed to be connectively stable with maximized interconnection bounds.