Asymptotical stability analysis of “PD+” controller for spacecraft attitude tracking system*

To overcome the difficulty that the asymptotical stability of spacecraft attitude tracking system, when “PD+” controller is employed, cannot be obtained by directly using common Lyapunov's theorems, several methods are introduced and summarized. Owing to the powerful features of Matrosov's theorem and Barbalat's lemma in the field of non-autonomous system stability analysis, they are respectively utilized to acquire the results of asymptotical stability of spacecraft attitude tracking system to which a common “PD+” controller is applied. Further more, to simplify the stability analysis, another special “PD+” controller is designed, by virtue of an auxiliary variable, and the corresponding stability analysis and comparisons with the preceding two methods are given as well.