Adaptive Disturbance Observer Design for Discrete-Time High-Order Fully Actuated Systems Based on LMI and Its Application to Combined Spacecrafts

This paper presents a study on the design of an adaptive disturbance observer for discrete-time high-order fully actuated (HOFA) systems, with application to the combined spacecraft simulator system. Firstly, a step backward HOFA model is introduced, which accounts for input uncertainty and external disturbance. Then, an adaptive disturbance observer based control (ADOBC) is developed using Lyapunov theories, ensuring that the resulting closed-loop system is asymptotically stable and that the output of the observer can track the disturbance. The feedback control matrices and the observer gain matrices are then obtained by solving a linear matrix inequality (LMI). Finally, the proposed approach is implemented in the combined spacecraft simulator, demonstrating its effectiveness.