This study presents an adaptive control scheme based on synergetic control theory for
suppressing the vibration of building structures due to earthquake. The control key for the
proposed controller is based on a magneto-rheological (MR) damper, which supports the
building. According to Lyapunov-based stability analysis, an adaptive synergetic control
(ASC) strategy was established under variation of the stiffness and viscosity coefficients in
the vibrated building. The control and adaptive laws of the ASC were developed to ensure …