Complete rejection of periodic disturbances in time-delay systems

The equivalent-input-disturbance (EID) approach is presented for time-delay systems with periodic disturbances in this paper. For the construction and the stability analysis with traditional equivalent-input-disturbance (EID) methodology being inadequate in time-delay systems, we propose a new configuration to reject periodic disturbances. First, we change the conventional EID estimator to be a repetitive controller to compensate for periodic disturbances. Then, to guarantee stability of the system, we present the analysis on stabilization condition with time-delay considered using linear-matrix-inequality (LMI), and derive a state feedback controller. At last, the simulation results demonstrate the validity of the proposed method by comparing with the traditional EID control method.