Quaternion-based H∞ kinematic attitude control subjected to input time-varying delays

In this paper, a quaternion-based H_∞ controller is proposed for the stabilization of rigid-body attitude kinematics subject to unknown time-varying delays. This work is motivated both by the applicability to practical scenarios where large measurement and communication delays are often time-varying and by the absence of results in the literature. The difficulties stem from the non-Euclidean manifold of unit quaternions and the nonlinearities inherent to the quaternion kinematics. They yield additional constraints to the time-delay analysis which in turn restricts the application of existing techniques-suitable for Euclidean space ℝⁿ-to investigate the time-varying delay. This paper exploits particular properties of unit quaternions in order to adapt such techniques whereby the stability criterion for time-varying delays is derived. In addition, the design criterion also satisfies performance properties in the H_∞ sense. The H_∞ control criterion is presented in the form of linear matrix inequalities (LMIs), providing efficient tools to obtain the controllers. The effectiveness of the proposed criterion is illustrated through numerical simulations.