A necessary and sufficient condition for output feedback stabilizability

In this paper, we deal with the attitude control of a satellite equipped with wheels of reaction, using the static output feedback. In the first part, we set the control and its integral in the state-feedback form. Then, by using the algorithm of Kucera, we establish the necessary and sufficient conditions so that the nonlinear system which models the satellite will be stabilizable by the Static Output Feedback. Thereafter, we present the robust stabilization of the attitude control; this robustness is influenced by the parametric uncertainly of the model and by the input noise in the system. The main results of this paper show that the sufficient conditions for the existence of the robust static output feedback control can stabilize the studied system. The controller proposed here is based upon a generalization of Gronwall’s lemma.