Global stabilization of nonlinear systems with a class of unmatched uncertainties

Global asymptotic stabilization of an uncertain dynamical system which violates the matching conditions is investigated. A class of unmatched uncertainties, called equivalently matched uncertainties, is defined. A robust controller is proposed to stabilize the uncertain system asymptotically in the large provided that the nominal system is uniformly asymptotically stable and that the unmatched uncertainties are equivalently matched. The required information about uncertain dynamics in the system is merely that the uncertainties are bounded in Euclidean norm by known functions of the system state