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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.

### MSC:

93D15 | Stabilization of systems by feedback |

93C41 | Control/observation systems with incomplete information |

### Keywords:

Global stabilization; Finite-time convergence; Hölder continuous state feedback; Lyapunov stability; Uncertain nonlinear systems### References:

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