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Mathematics 2016, 4(4), 58; doi:10.3390/math4040058

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

1
Polytechnical School of Tunisia, B.P. 743, La Marsa 2078, Tunis, Tunisia
2
LAIMI Laboratory, University of Quebec at Chicoutimi, Chicoutimi, QC G7H 2B1, Canada
*
Author to whom correspondence should be addressed.
Academic Editor: Johnny Henderson
Received: 17 June 2016 / Revised: 22 August 2016 / Accepted: 13 September 2016 / Published: 24 September 2016
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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 nonlinear systems. View Full-Text
Keywords: finite-time control; nonlinear system; non-Lipschitzian dynamics; Lyapunov function finite-time control; nonlinear system; non-Lipschitzian dynamics; Lyapunov function
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

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

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