Triaxial Stabilization of a Rigid Body via a Delayed Feedback Law

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Abstract
Two approaches to the problem of triaxial stabilization of a rigid body with the aid of delayed feedback law are considered. The first approach is based on choosing control as a sum of dissipative and restoring torques with a constant delay in the restoring torque. In this case, a special construction of Lyapunov–Krasovskii functional is used to derive exponential stability conditions of the programed regime. In the second approach, the control is constructed without using a dissipative torque. The stabilization is ensured via artificially introducing a delay in the restoring torque, and the proof of the exponential stability is based on the application of the Razumikhin method.

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