  The foremost aim of this study is to investigate the influence of
time-delayed feedback on extreme events in a non-polynomial system with
velocity dependent potential. To begin, we investigate the effect of this
feedback on extreme events for four different values of the external forcing
parameter. Among these four values, in the absence of time-delayed feedback,
for two values, the system does not exhibit extreme events and for the other
two values, the system exhibits extreme events. On the introduction of
time-delayed feedback and varying the feedback strength, we found that extreme
events get suppressed as well as get induced. When the feedback is positive,
suppression occurs for a larger parameter region whereas in the case of
negative feedback it is restricted to the limited parameter region. We confirm
our results through Lyapunov exponents, probability density function of peaks,
$d_{max}$ plot and two parameter probability plot. Finally, we analyze the
changes in the overall dynamics of this system under the influence of
time-delayed feedback. We notice that complete suppression of chaos occurs in
the considered system for higher values of the time-delayed feedback.
