In this paper, the control problem of a class of nonlinear systems with uncertainties is investigated, and synthesis techniques are developed under the assumption of so-called incomplete matching conditions. Nonlinear state feedback, based on differential geometry, is utilised to linearise the nominal part of the system and guarantee that the nominal closed-loop system has the desired stability margin. Additional nonlinear feedback is introduced to compensate for uncertainties, and stability is guaranteed via the theory of Lyapunov. The technique is applied, for illustrative purposes, to two situations, a straightforward nonlinear case, and a linear unstable case.
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