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This study investigates an important and challenging problem in non-linear systems: achieving output tracking control with a tolerable error bound as well as providing enhanced damping control of the internal dynamics. This problem is solved by using a damping controller in an input-output linearised static synchronous compensator system. The controllability and observability analyses direct the authors how to determine the damping controller gain. The proposed controller provides improved damping for lightly damped internal dynamics with degraded but tolerable output tracking performance. Finding a parameter-dependent Lyapunov function for the zero dynamics of error dynamics proves the stability of the damped internal dynamics in the time-invariant and time-varying systems. Stability of the closed-loop system is established by designing a composite Lyapunov function and it ensures that the tracking error of the output, in the approximated input-output linearised system, remains within a specified bound. Through stability analysis, the damping controller and the desired reference trajectory providing uniform boundedness of tracking error in output can be designed.