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.

中文翻译：

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使用延迟控制输入和状态误差的重复控制系统设计

本文提出了一种改进的重复控制方案，包括状态误差和通过延迟反馈的控制输入，以跟踪周期性参考轨迹和/或衰减干扰。闭环状态误差动态可以使用典型的中性延迟系统来表示，外源输入被衰减。通过应用 Lyapunov-Krasovskii 泛函和哈密顿量推导出实现整体稳定性和 H∞ 性能以最小化状态误差的充分条件，它们表示为代数 Riccati 不等式 (ARI) 和线性矩阵不等式 (LMI)。基于导出的条件，表明重复控制器设计问题可以重新表述为具有 LMI 约束的优化问题，以确定状态误差反馈增益。最后，