Generalized negative imaginary synthesis for attitude stabilization of flexible satellites with negative imaginary uncertainty

This paper studies the attitude control of a class of flexible satellites with negative imaginary (NI) uncertainty and proposes a new NI synthesis method for linear time invariant (LTI) system with two poles at the origin. Firstly, a dynamic parallel feedforward compensator is added to the controlled plant, which ensures that the augmented system exhibits negative imaginary property. Furthermore, a set of linear matrix inequalities (LMIs) conditions are derived, leading to easy application of this scheme. Secondly, a nonlinear numerical optimization method is adopted to design a set of strictly negative imaginary (SNI) controllers. An integral resonant controller is designed with internal stability and the worst-case $H_2$ norm of the closed-loop system minimized. Finally, a two-body flexible satellite simulation experiment is carried out to verify the effectiveness of the proposed method. The results show that the robust stability of the scheme is significantly better than that of the traditional robust control scheme in the case of parameter perturbation or unmodeled dynamics.