Design of Repetitive Control Systems Using a Delayed Control Input and a State Error

This paper presents a modified repetitive control scheme comprising of a state error and a control input via delayed feedback to track periodic reference trajectories and/or attenuate disturbances. The closed-loop state error dynamics can be represented using a typical neutral delay system with an exogenous input to be attenuated. The sufficient conditions to achieve overall stability and H_∞ performance to minimize state error are derived by applying a Lyapunov-Krasovskii functional and a Hamiltonian, which are expressed as an algebraic Riccati inequality (ARI) and a linear matrix inequality (LMI). Based on the derived conditions, it is shown that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint to determine the state error feedback gain. Finally, a numerical example is presented to demonstrate the feasibility of the proposed method.