Abstract:A new design method for linear system with model uncertainty is presented to restrain the external disturbance,which can design the repetitive controller and the output feedback controller simultaneously.The disturbance rejection problem of the linear system is reformulated as a robust stability problem of the system with structured uncertainties through introducing a fictitious uncertainty.Using small gain theorem,a sufficient condition is derived,which ensures robust stability of the system with structured uncertainties.A stable matrix is introduced to get a sufficient condition with less conservativeness for the system with structured uncertainties.Basing on the resulting sufficient condition,by using linear matrix inequality(LMI) and cone complementarity linearization(CCL),an iterative algorithm is presented to calculate the largest cut-off frequency of the low-pass filter in the repetitive controller and the parameters of the output feedback controller simultaneously.Finally,the validity of this method is verified by a low-frequency linear vibration table system.