Enhanced LMI-Based composite nonlinear control for a knee rehabilitation exoskeleton robot considering motion constraints

This paper proposes a novel robust control strategy for the stabilization of a knee rehabilitation exoskeleton robot. Unlike traditional methods, the designed controller combines a linear state-feedback law with a nonlinear compensation term to effectively address the robot’s nonlinear dynamics under parameter uncertainties, external disturbances, and motion constraints. Two complementary approaches are introduced: one assumes a constant bound on the nonlinearities and another employs a state-dependent linear constraint. For each approach, tailored Linear Matrix Inequality (LMI) conditions are derived using specific technical lemmas, including Young’s inequality, the S-procedure, the Schur complement, and the matrix inversion lemma. The originality of this work lies in the systematic integration of motion constraints and external disturbances into the LMI framework for composite control. Numerical simulations validate the proposed methodology, thereby demonstrating superior robustness and stability performance compared to conventional control strategies.