# Robust stochastic stabilization of attitude motion

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## Abstract

This study proposes robust stochastic stabilization of rigid body attitude motion within the framework of geometric mechanics, which can globally represent the attitude dynamics model. The system is subject to a stochastic input torque with an unknown variance parameter and an unknown nonlinear diffusion coefficient matrix. Our development starts with introducing a general notion of the stochastic stability in probability within the framework of geometric mechanics. Then, the Morse–Lyapunov (M–L) technique is employed to design a nonlinear continuous stochastic feedback control law. Finally, the asymptotic stability of the system is guaranteed in probability and the control gain parameters are obtained via solving a linear matrix inequality feasibility problem. An estimate of the region of attraction of the system is calculated to provide a better insight for tuning the control gain parameters. Two illustrative examples are performed based on the discretized model of the closed-loop system to demonstrate the effectiveness of the proposed control scheme.

## Keywords

Attitude motion Stochastic stabilization Morse–Lyapunov function Region of attraction Geometric mechanics## Notes

### Acknowledgements

Financial support from the National Science Foundation under Grant No. CMMI-1131646 is gratefully acknowledged.

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