Semi-global stabilisation of uncertain non-linear systems by homogeneous output feedback controllers

This study considers the problem of semi-global finite-time stabilisation by output feedback for a class of uncertain non-linear systems with both higher-order and lower-order terms, to which the existing design schemes are inapplicable. Based on the homogeneous domination approach, a scaled homogeneous output feedback controller is constructed to semi-globally stabilise the system in a finite time by choosing an appropriate gain. The proposed approach not only achieves finite-time convergence, but also widens the applicability to broader classes of systems with mixed-order non-linearities and a non-triangular structure.