This paper investigates robust asymptotic stabilization of rigid body attitude dynamics evolving on the tangent bundle of SO(3) using geometric stochastic feedback control, where the system is subject to a stochastic input torque. To start with, the attitude dynamics is interpreted in the Ito sense. However, due to evolution of the kinematic differential equation of the system on SO(3), analyzing the stochastic system on TSO(3) is non-trivial. To address this challenging problem of robust asymptotic stabilization of attitude dynamics, the back-stepping method along with a suitable Morse-Lyapunov (M-L) function candidate with constant control gain parameters are used to obtain a nonlinear stochastic feedback control law. The control gain matrix and the M-L function control gain can be obtained by solving a feasible LMI, which can guarantee the robust asymptotic stability of the rigid body on TSO(3). Numerical simulations are performed to demonstrate and validate the effectiveness of the proposed controller in the state space of rigid body attitude motion in TSO(3).
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