Attitude control and stabilization of a micro-satellite is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites' state-space model. In this article a novel nonlinear optimal (H-infinty) control approach is developed for this control problem. The dynamic model of the satellite's attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite's attitude. For the approximately linearized description of the satellite's attitude a stabilizing H-infinity feedback controller is designed. To compute the controller's feedback gains an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control, that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.