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Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

Author

Listed:
  • Nawel Khelil

    (Polytechnical School of Tunisia, B.P. 743, La Marsa 2078, Tunis, Tunisia)

  • Martin J.-D. Otis

    (LAIMI Laboratory, University of Quebec at Chicoutimi, Chicoutimi, QC G7H 2B1, Canada)

Abstract

This paper focuses on the problem of finite-time stabilization of homogeneous, non-Lipschitz systems with dilations. A key contribution of this paper is the design of a virtual recursive Hölder , non-Lipschitz state feedback, which renders the non-Lipschitz systems in the special case dominated by a lower-triangular nonlinear system finite-time stable. The proof is based on a recursive design algorithm developed recently to construct the virtual Hölder continuous, finite-time stabilizer as well as a C 1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz nonlinear systems.

Suggested Citation

  • Nawel Khelil & Martin J.-D. Otis, 2016. "Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems," Mathematics, MDPI, vol. 4(4), pages 1-14, September.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:4:p:58-:d:78836
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