In this paper, a kind of robust observer design scheme based on a constrained Lyapunov equation is presented for a class of non-linear interconnected systems using structural characteristics. The non-linear interconnected system is not required to be affine or linearizable. Both matched and unmatched uncertainties are considered, and a method to deal with uncertain interconnections is proposed. The bounding functions of all the uncertainties may be arbitrarily large since non-linear gain functions are introduced to eliminate the effects of the uncertainties by exploiting their structural characteristics. Simulation is given to demonstrate the effectiveness of the proposed scheme.