In this article, we present a relay control scheme based on LQR design with fast convergence. This scheme provides a practical and simple way to achieve fast convergence based on the well-known LQR design principle. The controller is a global stabiliser in the sense that for any given initial condition, we can always initialize the controller to drive the system to reach the origin. ; This controller is tunable in accordance with the position of the system state: the closer to the origin, the larger the control gains, which results in a fast control that maintains bounded control magnitude. It has also been shown that setting matrix Q can significantly influence the tendency of eigenvalues to switch the hyperplane. The relation between matrix Q and the tendency of those eigenvalues has been identified. Simulation results are presented to demonstrate the effectiveness of the scheme.