A Robust LMI-Based Approach for the Position Control of a 1-DoF Knee Rehabilitation Exoskeleton Robot Considering State Constraints

This study introduces a robust control strategy designed for a one-degree-of-freedom (1-DoF) knee rehabilitation exoskeleton robot. Focusing on position control, our approach addresses challenges such as state constraints, parameter uncertainties, solid and viscous frictions, and external disturbances. To achieve this goal, we propose an affine state-feedback controller. Additionally, utilizing a quadratic Lyapunov function, we establish some Linear Matrix Inequality (LMI) stability conditions on the matrix gain of the adopted controller to ensure robust stabilization of the robot to the desired position. These conditions are developed using some mathematical tools and congruence transformations. Finally, some results are presented to show the validity and efficiency of the controller in achieving robust stabilization of the 1-DoF knee exoskeleton robot, even under uncertainties and external disturbances.