A completely decentralised observer-based control scheme for interconnected dynamical systems is proposed. The scheme requires no information transfer among the subsystems, local observers or local controllers and applies equally to systems with known and/or unknown disturbances. It is shown that each local observer asymptotically converges to the true state of its corresponding subsystem and, on satisfaction of some mild controllability and observability conditions, local stabilising feedback controllers can be designed in isolation of the local observers. A numerical example with simulation results is given to illustrate the effectiveness of the new approach.