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Finite-time stabilization of nonlinear quadratic systems by a non linear state feedback

This paper investigates the synthesis of sufficient conditions for finite-time stabilization of nonlinear quadratic systems via a nonlinear static state controller. For this purpose, we consider polytopic domains rather than ellipsoidal domains, and we investigate the usefulness of combining the notion of annihilator with a version of Finsler's Lemma. The design conditions obtained are expressed in term of state-dependent Linear Matrix Inequalities.