Abstract:Aiming at suppressing the amplitude and time of oscillation, the uncertainties of the disturbance of unknown external disturbances of the stay cable-magnetorheological damper control system and uncertainties in the parameters of the damping controller. Based on linear matrix inequality (LMI) theory, the H∞ performance index and nonfragile control were used to suppress external disturbances and closed-loop system parameter perturbation problems, respectively. Regional pole configuration was used to characterize the fastness and stability of vibration reduction control, and variance was used to represent small amplitude and vibration speed. The LMI toolbox in Matlab was used to solve the convex optimization problem with multiple LMI constraints and linear objective functions, and a non-fragile vibration damping controller design form with multiple performance index constraints was given. Finally, the cablestayed cables C22 and C13 of a crosssea bridge in Zhejiang Province were taken as an example for simulation verification, and the vibration reduction effects were analyzed and compared. The results showed that the vibration damping controller designed by this method not only had good immunity and stability under different random disturbances, but also could reduce the amplitudes of different cable vibration states by 57.805% and 74.395%, the reduction of convergence time was 56.705% and 77.845%, and the vibration reduction effect was better, which could meet the needs of marine engineering applications.