This paper addresses the problem of feedback stabilization of the Brockett integrator within the framework of nonregular feedback linearization. First, the nonsmooth version of nonregular feedback linearization is formulated, and a criterion for nonregular feedback linearization is presented. Then, it is proven that the Brockett integrator is nonregular state feedback linearizable, thus enable us to design feedback control law using standard techniques of linear systems. The obtained discontinuous control laws guarantee convergence of the closed-loop system with exponential rates. Finally, simulation results are presented to illustrate the effectiveness of the proposed control laws.
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