Attitude Stabilization with Unknown Bounded Delay in Feedback Control Implementation

This paper addresses the problem of stabilizing attitude dynamics with an unknown constant delay in feedback with a known strict upper bound. A novel modification to the concept of the complete-type Lyapunov―Krasovskii functional plays a crucial role toward ensuring stability robustness to time delay in the control design. The control law is linear in states, and the resulting closed-loop equations are partitioned to form a nominal system with a perturbation. After obtaining necessary and sufficient exponential stability conditions for the nominal system, a complete-type Lyapunov―Krasovskii functional is constructed. As an intermediate step, an analytical solution for the underlying Lyapunov matrix is obtained. A systematic numerical optimization process is employed here to choose various controller gain parameters so that the region of attraction estimate is maximized. The closed-loop dynamics are shown to be exponentially stable inside the region of attraction estimate. To the authors' best knowledge, this is the first result that provides stable closed-loop control design for the attitude dynamics problem with an unknown delay in feedback.