H_∞ Synthesis for satellite formation keeping: An LMI approach

Numerous controllers have been proposed based on linear Hill's equations for satellite formation control. To date, most of these controllers assumed that the system model is well defined, and the disturbances are small. Previous studies have failed to consider the problem of disturbance rejection. In this paper, Ho controllers are designed for disturbance attenuation based on linear Hill's equations. The goal is to design a state-feedback control law which minimizes the H_∞ norm of transfer function from disturbance to the regulated outputs, which guarantee stable for the closed-loop system. The problem is reduced to a convex optimization involving linear matrix inequalities (LMIs). The proposed robust controllers are evaluated in simulation. The simulation results demonstrate that the proposed controllers are capable of controlling the satellite formation system more precisely than LQR under various perturbations.