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In order to achieve global stability at the origin of the system, a feedback controller can be designed using the backstepping method. This method involves constructing a Lyapunov function that satisfies certain conditions, and then designing a controller based on the derivative of the Lyapunov function. The resulting controller can adjust the system's state in response to changes in the input or disturbances, and can ensure that the system remains stable over time. Additionally, it may be possible to optimize the controller's performance by adjusting certain parameters or using advanced techniques such as adaptive control or nonlinear control. Overall, the use of feedback control can greatly enhance the stability and performance of dynamic systems, making them more robust and reliable in a wide range of applications.