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Static synchronous compensator (STATCOM) is a non-linear system so that the conventional linear output feedback controller with synthesised feedback control cannot guarantee uniform tracking performance, although it improves the stability margin in an inductive operating range. Recently, the input-output linearisation via feedback has been applied to STATCOM and it shows uniform transient performance but owing to lightly damped internal dynamics it results in current ripples in DC-side capacitors. To reduce the ripples, a damping term, time derivative of active current multiplied by a constant gain, was added to the input-output linearisation. This damping controller brings improved internal stability by moving the poles of internal dynamics from the imaginary axis. However, there exists one important limitation that it cannot guarantee stability of internal dynamics at every operating point for some system parameters. A modified non-linear damping controller is proposed to improve the limitation. The proposed method has the damping term with a variable gain, thus provides improved transient performance over the whole operating range. Stability of the closed-loop system is verified by the parameter-dependent Lyapunov function. Owing to the damping term, the exact input-output linearisation is not performed; thus the output is not decoupled from internal dynamics and oscillatory transient response appears. Using the parameter-dependent Lyapunov function, it is also shown that the oscillatory output response is bounded. Improved transient performance in time-domain is validated by simulations with the topological model.