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.