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Open AccessFeature PaperArticle

Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

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Polytechnical School of Tunisia, B.P. 743, La Marsa 2078, Tunis, Tunisia
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LAIMI Laboratory, University of Quebec at Chicoutimi, Chicoutimi, QC G7H 2B1, Canada
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Author to whom correspondence should be addressed.
Academic Editor: Johnny Henderson
Mathematics 2016, 4(4), 58; https://doi.org/10.3390/math4040058
Received: 17 June 2016 / Revised: 22 August 2016 / Accepted: 13 September 2016 / Published: 24 September 2016
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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Khelil, N.; Otis, M.J.-D. Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems. Mathematics 2016, 4, 58.

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