Global stabilization of the linearized three-axis axisymmetric spacecraft attitude control system by bounded linear feedback

In this paper, the three-axis attitude stabilization of the axisymmetric spacecraft with bounded inputs is studied. By constructing some novel state transformations, saturated linear state feedback controllers are constructed for the considered attitude control system. By constructing suitable quadratic plus integral Lyapunov functions, globally asymptotic stability of the closed-loop systems is proved if the feedback gain parameters satisfy some explicit conditions. By solving some min-max optimization problems, a global optimal feedback gain for the underactuated attitude stabilization system is proposed such that the convergence rate of the linearized closed-loop system is maximized. Numerical simulations show the effectiveness of the proposed approaches.