Homogeneous Unit Sliding Mode Control for Uncertain Mechanical Systems

This paper introduces the concept of high‐order convex approximation to address uncertainties in a class of nonlinear uncertain mechanical systems. Based on this concept, the homogeneous unit sliding mode control (HUSMC) is designed to handle multiplicative and additive perturbations (uncertainties and disturbances) of the plant. By integrating this design methodology within the framework of linear matrix inequalities (LMIs), we achieve precise adjustments to control parameters, thereby enhancing tracking accuracy and stability. Numerical simulations of an uncertain mechanical system demonstrate the effectiveness of the proposed method in mitigating uncertainties and ensuring the desired control accuracy.