Discontinuous feedback for high-order uncertain systems in power chained form

This paper studies the problem of almost asymptotic stabilization for a lass of high-order uncertain systems in power chained form perturbed by a triangular vector field. The particular nonlinear system in this note is lack of affineness in the control input and cannot been handled by any smooth state feedback control law. We utilize a discontinuous change of coordinates and adding a power integrator technique under the aid of a set of sufficient conditions. Finally, we construct discontinuous controllers and complete the systematic almost stabilization and adaptive regulation. We also present how the results can be extend from the linear perturbation to the parameterized one.