Convex Optimization of a Spacecraft Stabilization with a Double-Gimbal Variable-Speed Control Moment Gyro Actuator: Geometric Approach

This paper applies the linear parameter-varying (LPV) control theory to the attitude stabilization problem for a spacecraft with a double-gimbal variable-speed control moment gyro (DGVSCMG). The LPV control theory can provide an optimal gain-scheduled (GS) controller by using linear matrix inequalities (LMIs) with regional pole placement constraints. When LMIs are solved, most studies select a common Lyapunov function for the whole operating range. However, selecting a common Lyapunov function leads to conservatism of design. The scheduling parameters in the LPV model of a spacecraft with a DGVSCMG have an interesting property. By using this property, this paper proposes the method to geometrically reduce the number of vertices in the convex hull to cover the LPV system. Through numerical examples, the proposed method can reduce the conservatism of design.