A nonlinear optimal (H-infinity) control approach is proposed for an electric power unit that comprises a gas-turbine and a synchronous-generator. The control method aims at synchronizing the generator with the grid's frequency while also optimizing the fuel's consumption by the gas-turbine. At a first stage the state-space model of the the power unit is linearized at a temporary operating point which is updated at each iteration of the control method. The linearization procedure relies on Taylor series expansion and on the computation of the system's Jacobian matrices. At a second stage, an H-infinity feedback controller is designed for the approximately linearized model of the power unit. This allows to solve the optimal control problem of the power generation unit, despite the effects of model inaccuracy and exogenous disturbances. The feedback gain of the H-infinity controller, is obtained after solving an algebraic Riccati equation at each time-step of the control method. Finally, Lyapunov analysis is used to prove the global asymptotic stability properties of the control scheme.