This paper proposes a novel distributed estimation and control method for uncertain plants. It is of application in the case of large-scale systems, where each control unit is assumed to have access only to a subset of the plant outputs, and possibly controls a restricted subset of input channels. A constrained communication topology between nodes is considered so the units can benefit from estimates of neighboring nodes to build their own estimates. The paper proposes a methodology to design a distributed control structure so that the system is asymptotically driven to equilibrium with L2-gain disturbance rejection capabilities. A difficulty that arises is that the separation principle does not hold, as every single unit ignores the control action that other units might be applying. To overcome this, a two-stage design is proposed: firstly, the distributed controllers are obtained to robustly stabilize the plant despite the observation errors in the controlled output. At the second stage, the distributed observers are designed aiming to minimize the effects of the communication noise in the observation error. Both stages are formulated in terms of linear matrix inequalities. The performance is shown on a level-control real plant.