A systematic approach for robust repetitive controller design

•A detailed analysis to illustrate the impact of the repetitive structure.•Systematic design procedure by solving a convex optimization problem.•Focus on the application aspects of the proposed method.•Experimental results in a commercial 4.3 kVA PWM single phase DC–AC inverter.•Results analyzed under performance criteria defined by the IEC 62040-3 standard.

In this paper, a methodology for the synthesis of repetitive controllers to ensure periodic reference tracking and harmonic disturbance rejection is cast in a robust control framework. Specifically, the Lyapunov–Krasovskii theory is applied to derive LMI-based conditions for designing a state feedback control law with guaranteed stability and performance properties for system parameter variations. Practical experiments in commercial uninterruptible power supplies – UPS are considered to illustrate and discuss some practical implementation aspects of the proposed method.