This paper presents the design of a robust decentralized controller for the frequency and active power control of a single stand-alone (off-grid) mechanically-coupled generator system including wind turbine and diesel engine generator subsystems. Two robust decentralized controllers are designed and optimized for the two subsystems by using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> -synthesis technique. The decentralized controllers address the mechanical coupling between the two subsystems without communicating with each other. In addition, both controllers are designed in such a way that they are robust against the concurrent variations of all the system parameters, which in turn improves the frequency and power control performances significantly. Simulation results indicate that the proposed decentralized controllers have a better performance as compared to the benchmark decentralized model predictive controllers and decentralized linear-quadratic Gaussian controllers. It is also demonstrated that the proposed control scheme is able to damp out mild and large disturbances originating from the load and wind power changes, and has an acceptable robust performance against the concurrent variations in all parameters of the system.