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Global finite-time stabilization of a class of uncertain nonlinear systems. (English) Zbl 1098.93032
Summary: This paper studies the problem of finite-time stabilization for nonlinear systems. We prove that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Hölder continuous state feedback. The proof is based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently for the control of inherently nonlinear systems that cannot be dealt with by any smooth feedback. A recursive design algorithm is developed for the construction of a Hölder continuous, global finite-time stabilizer as well as a C 1 positive definite and proper Lyapunov function that guarantees finite-time stability.

93D15Stabilization of systems by feedback
93C41Control problems with incomplete information