Estimating the stability domain of spacecraft attitude with delayed feedback

This study deals with the estimation of the stability domain of the spacecraft attitude control system with delayed feedback. For autonomous functional-differential equations, by using the invariance principle, a general estimation theorem is established to explicitly estimate the stability domain. Furthermore, based on the estimation theorem and an applicable Lyapunov functional, an estimation criterion of the stability domain for the spacecraft attitude control system with delayed proportional-derivative (PD) controller is obtained. It is worth noting that the estimation criterion can be described as a generalised eigenvalue problem and thus can be solved by linear matrix inequality (LMI) optimisation techniques. Finally, numerical examples show the effectiveness of the estimation criterion.