Magnetic Attitude Control of Bias Momentum Spacecraft by Bounded Linear Feedback

This paper addresses the three-axis magnetic attitude control of small spacecraft with momentum bias configuration by bounded linear feedback. Necessary and sufficient conditions are derived to guarantee that the linearized dynamics and kinematics are stable in the Lyapunov sense. Explicit solutions to some Lyapunov equations associated with the considered open-loop system are obtained. Based on the explicit solutions to the Lyapunov equation, an explicit saturated linear state feedback controller is designed. Globally asymptotic stability of the closed-loop systems is proved by constructing the explicit Lyapunov function. Simulations show the effectiveness of the proposed approach.