Robust Controller Design for Attitude Dynamics Subjected to Time-Delayed State Measurements

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Attitude control and time-delay systems are well-developed fields in the control theory, but only a modicum of papers have explored control systems that fall within the intersection of the two. Indeed, combining kinematics and dynamics nonlinearities with sensor and actuator delays reinvigorates the original attitude control problem, typically leading to involved stability arguments based on nonlinear analysis techniques. This paper instead proposes solving the attitude stabilizer design problem by formulating it as a linear matrix inequality feasibility problem. The proposed approach simplifies the stability arguments, without loosing generality; the obtained conditions cope with the general case of rigid bodies that suffer from unknown, heterogeneous, time-varying state measurement delays, and have inertia uncertainties. This methodology is particularly well suited to resource-limited applications, because controllers can be designed offline using computationally efficient tools. Although simple, numerical evidence shows the stability criterion derived in this paper largely outperforms previous results.