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Reduced-order observer, homogeneous domination and nonsmooth output feedback stabilization of nonlinear systems

In this paper, we study the problem of global stabilization by output feedback for a general class of non-uniformly observable and non-smoothly stabilizable systems with uncertainty. By using a homogeneous domination method, together with a recursive design for the construction of reduced-order observers, we prove that the problem is solvable for a large family of genuinely nonlinear systems with both lower- and higher-order nonlinearities. The focus of this work is to exploit the idea of how to deal with polynomial growth nonlinearities via domination and homogeneity.