A robust H-2 controller is designed using an LMI-based technique. In this approach, the controller synthesis is similar to an LQR, but with the possibility of considering parametric uncertainties. The designed controller is applied to a reaction wheel unicycle robot, which is an unstable and sensitive system in terms of parametric errors. An implementation aspect regarding the dynamic torque limitation of the reaction wheel actuator is emphasised. Since the equivalent linear model is decoupled, a decentralised controller structure is fixed during the synthesis. Simulation and practical results are shown. A detailed description of the robot construction is also presented.