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Time-Delayed Gyro-Free Attitude Stabilization

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Abstract

This paper addresses output feedback stabilization of fully actuated rigid-body attitude dynamics in the presence of unknown point-wise time-delay in the input torque. Specifically, rate-gyros are unavailable here and only the attitude state represented by the unit quaternion is assumed to be measured. In the absence of time-delay, it is well known that linear asymptotically stabilizing control laws can be derived for this problem using the passivity properties of the system. The presence of unknown time-delay in the measured variables, however, imposes formidable technical challenges for the output-feedback attitude stabilization problem on hand. One of the central difficulties stems from the availability of only a weak Lyapunov-like function for the passivity based dynamic output feedback controller in the absence of delay. This obstacle is circumvented in this paper by a novel process of partially strictifying the underlying weak Lyapunov-like function. This step lends itself very nicely toward the subsequent definition of a Lyapunov-Krasovskii type functional when unknown time-delay is introduced within the feedback. The paper concludes with a closed-loop stability analysis that includes a rigorous characterization for the region of attraction as a function of the initial angular speed and the magnitude of the time-delay.
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Dates and versions

hal-01211536 , version 1 (05-10-2015)

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Frédéric Mazenc, Sungpil Yang, Maruthi Akella. Time-Delayed Gyro-Free Attitude Stabilization. 2015 American Control Conference (ACC), Jul 2015, Chicago, United States. pp.3206 - 3211, ⟨10.1109/ACC.2015.7171826⟩. ⟨hal-01211536⟩
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