Finite-Time Stabilization of Homogeneous Non-Lipschitz Systems

Nawel Khelil and Martin J.-D. Otis
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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

Mathematics, 2016, vol. 4, issue 4, 1-14

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.

Keywords: finite-time control; nonlinear system; non-Lipschitzian dynamics; Lyapunov function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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