A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems

In this paper, a novel systematic design method, namely homogeneous domination approach, is developed for the global output feedback stabilization of nonlinear systems. The nonlinearities of the systems considered in this paper are neither linearly growing nor Lipschitz in immeasurable states, which make the most of existing methods inapplicable to solve the problem. By utilizing the homogeneous domination approach, a global output feedback stabilizer is explicitly constructed in two steps: i) we first design for the nominal linear system a unique homogeneous output feedback controller whose construction is genuinely nonlinear, rather than linear as used in the literature; ii) then we scale the homogeneous observer and controller with an appropriate choice of gain to render the nonlinear system globally asymptotically stable. The homogeneous domination approach not only enables us to completely remove the linear growth condition, which has been the common assumption for global output feedback stabilization, but also provides us a new perspective to deal with the output feedback control problem for nonlinear systems.