Cascades stability analysis applied to a control design for unmatched perturbation rejection based on HOSM

We present preliminary results on exact stability of hierarchical high order sliding mode (HOSM) controlled systems with smooth perturbations. We solve the exact tracking control problem for triangular systems of second order hence, our results are a starting point for backstepping HOSM control. The approach is based on the so-called quasi-continuous high order sliding modes algorithm however, we relax the conservative assumption of boundedness of solutions. The stability analysis is based on cascaded systems theory for nonlinear time-varying Lipschitz systems.