Robust Position Control of a Knee-Joint Rehabilitation Exoskeleton Using a Linear Matrix Inequalities-Based Design Approach

This study focuses on developing a control methodology for exoskeleton robots designed for lower limb rehabilitation, specifically addressing the needs of elderly individuals and pediatric therapy. The approach centers on implementing an affine state-feedback controller to effectively regulate and stabilize the knee-joint exoskeleton robot at a desired position. The robot’s dynamics are nonlinear, accounting for unknown parameters, solid and viscous frictions, and external disturbances. To ensure robust stabilization, the Lyapunov approach is utilized to derive a set of Linear Matrix Inequality (LMI) conditions, guaranteeing the stability of the position error. The derivation of these LMI conditions is grounded in a comprehensive theoretical framework that employs advanced mathematical tools, including the matrix inversion lemma, Young’s inequality, the Schur complement, the S-procedure, and specific congruence transformations. Simulation results are presented to validate the proposed LMI conditions, demonstrating the effectiveness of the control strategy in achieving robust and accurate positioning of the lower limb rehabilitation exoskeleton robotic system. © 2025 by the authors.