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Normalised quadratic control, a modification of the conventional quadratic control method, has recently been proposed to exponentially stabilise a homogeneous bilinear system whose open-loop eigenvalues all fall on the imaginary axis. The normalised quadratic control method is now extended to a broader class of bilinear systems whose open-loop eigenvalues may fall to the left or right of the imaginary axis. It is shown that for bilinear systems that are already open-loop stable, the normalised quadratic control can add to the system an extra exponential decay rate. For open-loop unstable bilinear systems, the normalised quadratic control can stabilise the system if the extra exponential decay rate provided by the control is larger than the open-loop system's growth rate.