Finite-time stabilization of high-order sliding mode dynamics with lower-triangular structure

In this paper, the finite-time stabilization problem of high-order sliding-mode (HOSM) dynamics with lower-triangular structure is addressed. A new HOSM algorithm is proposed by means of the adding a power integrator technique. The proposed HOSM algorithm has two distinct features. First, the algorithm only requires that the mismatched uncertainties in the sliding mode dynamics satisfy some homogeneous growth conditions and thus removes the assumption that they should be sufficiently smooth. Second, for the matched uncertainties, the algorithm relaxes the constant upper bound assumptions adopted by most of the existing HOSM methods to the state-dependent hypotheses. Furthermore, the Lyapunov theory is utilized to establish the finite-time stability of the proposed HOSM algorithm. Finally, the validity of the proposed finite-time HOSM control method is demonstrated by simulation results