Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

中文翻译：

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基于 LMI 的膝关节康复外骨骼机器人位置控制鲁棒状态反馈控制器设计：比较分析

康复外骨骼机器人在恢复运动障碍患者的下肢功能性运动方面发挥着至关重要的作用。许多研究都集中在调整这些康复机器人系统的控制上。在本研究中，我们研究了用于膝外骨骼机器人鲁棒位置控制的仿射状态反馈控制律，并考虑了包括固体和粘性摩擦的非线性动态模型。为了确保鲁棒稳定性，我们采用了 Lyapunov 方法，并提出了三种方法来使用 Schur 补集、Young 不等式、矩阵求逆引理和 S 过程引理来建立稳定性条件。这些条件被表述为线性矩阵不等式 (LMI)。此外，我们对这些方法进行全面比较，以确定最有效的方法。在这项工作的最后，我们提出了仿真结果来验证所开发的 LMI 条件，并证明所采用的控制律在实现膝外骨骼机器人鲁棒位置控制方面的有效性。