Preprint Article Version 1 NOT YET PEER-REVIEWED

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

  1. Polytechnical School Of Tunisia, La Marsa, Tunis, Tunisia
  2. LAIMI Laboratory, University of Quebec at Chicoutimi, Quebec, QC G7H 2B1, Canada
Version 1 : Received: 1 August 2016 / Approved: 2 August 2016 / Online: 2 August 2016 (10:40:38 CEST)

A peer-reviewed article of this Preprint also exists.

Khelil, N.; Otis, M.J.-D. Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems. Mathematics 2016, 4, 58. Khelil, N.; Otis, M.J.-D. Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems. Mathematics 2016, 4, 58.

Journal reference: Mathematics 2016, 4, 58
DOI: 10.3390/math4040058

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 C1 positive definite and proper Lyapunov function that guarantees finite-time stability of the non-Lipschitz non-linear systems.

Subject Areas

Finite-time control; nonlinear system; non-Lipschitzian dynamics; lyapunov function

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