“…In the aforementioned structure, the vibration of a nine-story building exposed to an earthquake was tried to be damped via a Lyapunov-based adaptive control design based on the backstepping control approach. The use of the backstepping controller with ATMD systems for reducing vibration of buildings is very limited in the literature, but it is possible to find examples of use with magnetorheological dampers (Ali and Ramaswamy, 2009;Ouyang et al, 2019a;Shan et al, 2018;Zapateiro et al,2009) and active base isolators (Ouyang et al, 2019b;Pozo et al, 2006). In some studies (Amini and Ghaderi, 2013;Ghaderi and Amini, 2017), earthquake-induced vibrations were dampened by applying force to the multiple floors of the building, with actuators placed in another rigid structure by using the backstepping controller.…”