The dynamic model of the power unit undergoes approximate linearization around a temporary operating point (equilibrium) which is recomputed at each iteration of the control method. The linearization procedure is based on first-order Taylor-series expansion and on the computation of the Jacobian matrices of the joint turbine and generator's model. For the approximately linearized model of the power unit an H-infinity feedback controller is designed. This controller stands for the solution of the power unit's optimal control problem under model uncertainty and external disturbances. The computation of the controller's feedback gain requires the solution of an algebraic Riccati equation, which is performed again at each time-step of the control algorithm. The stability properties of the control scheme are proven trough Lyapunov analysis. First, it is confirmed that the controller satisfies the H-infinity tracking performance criterion which ascertains its robustness. Moreover, it is proven that the control loop is globally asymptotically stable. Finally, to implement sensorless control of the power unit the H-infinity Kalman Filter is used as a robust state estimator.