Time-delayed gyro-free attitude stabilization

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.