High‐Order Sliding‐Mode control for MIMO Systems

ABSTRACT

This paper extends Lyapunov‐based homogeneous high‐order sliding‐mode control to a class of uncertain non‐square multi‐input multi‐output (MIMO) nonlinear systems with a well‐defined vector relative degree. The considered systems admit a normal‐form representation with an uncertain but full‐row‐rank input‐gain matrix. Since this matrix is uncertain, channel decoupling cannot be guaranteed, and the main challenge is to cope with the resulting inter‐channel coupling. To address this issue, we generalize a control Lyapunov function (CLF)‐based methodology, previously developed for single‐input single‐output (SISO) systems, to the MIMO setting. The proposed framework yields a family of homogeneous discontinuous controllers ensuring robustness against bounded perturbations, as well as homogeneous continuous approximations that achieve practical stabilization while mitigating chattering. Numerical simulations validate the effectiveness of the proposed design.