This paper studies the global attitude stabilization of a rigid body, a task that is subjected to topological obstacles. These obstructions preclude the existence of a globally stable equilibrium point. Consequently, the rigid body attitude cannot be globally stabilized by continuous feedback control laws. Therefore, this paper presents an observer-based hybrid feedback control law to overcome the topological restrictions. In order to derive the proposed controller, a new kind of synergistic potential functions is designed which induces a gradient vector field to globally stabilize a given set. Moreover, the gradient of the proposed synergistic potential functions is utilized to introduce a hybrid angular velocity observer. Furthermore, this paper considers two types of constraints: angular velocity constraint, and torque constraint. Afterward, these constraints are formulated in terms of the Linear Matrix Inequalities (LMI) optimization problem to perform constraints satisfaction at all times. In addition, this paper introduces a novel hybrid quantizer to deal with the problem of the low-price wireless network. This paper analyzes the global asymptotic stability of the reference set via Lyapunov\\\'s method. Finally, a comparative study in simulations is provided to assess the performance of the proposed control technique.

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