The paper proposes a decentralized state estimation method for the control of multi-agent networked systems, where the goal is the tracking of arbitrary setpoint functions. The cooperative agents are partitioned into independent robots, providing the control inputs, and dependent robots, controlled by local interaction laws. The proposed state estimation algorithm allows the independent robots to estimate the state of the dependent robots in a completely decentralized way. To do that, it is necessary for each independent robot to estimate the control input components computed by the other independent robots, without requiring communication among the independent robots. The decentralized state estimator, including an input estimator, is developed and the convergence properties are studied. Simulation results show the effectiveness of the proposed approach.