Abstract
This paper investigates a generalized homogeneous adaptive stabilization method for a class of high-order nonlinear systems without controllable/observable linearizations. Based on a general approximated homogeneous function restraining hypothesis, a series of quasi-homogeneous adaptive virtual controllers are built. By modifying the homogenous domination approach, an inductive stability analysis as well as the guideline of update laws is carried out in an explicit way. Furthermore, based on the proposed design framework, the asymptotical and finite-time stabilization with the flexibility of tuning homogeneous degree are investigated. Numerical simulations and a real example are presented to demonstrate the effectiveness of the proposed method.