Gain-scheduled control of attitude of a satellite: Synthesis via G-scaling

This paper considers design of gain-scheduled controllers for attitude control of satellites whose inertia varies due to the rotation of the solar paddles. The control problem is reduced to solving a parameter-dependent LMI with the solar paddle angle as the scheduling parameter. The parameter-dependent LMI can be parameterized by trigonometric polynomials and the G-scaling leads to an equivalent parameter-independent LMI without any conservatism. This results a gain-scheduled controller whose coefficient matrices are trigonometric rational functions. The complexity of the coefficient matrices are reduced by using Fourier approximation, which derives gain-scheduled controllers whose coefficient matrices are low-order trigonometric polynomials or possibly constants with satisfactory control performances.