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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Sliding Mode Control of Fractional Lorenz-Stenflo Hyperchaotic System

Discontinuity, Nonlinearity, and Complexity 4(4) (2015) 445--455 | DOI:10.5890/DNC.2015.11.007

Jian Yuan; Bao Shi

Institute of System Science and Mathematics, Naval Aeronautical and Astronautical University, Yantai, 264001, China

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This paper proposes sliding mode control for the 4-D fractional order Lorenz-Stenflo hyperchaotic system. Two methods are utilized: one is based on the frequency distributed model of fractional integral operator; and the other is based on the Mittag-Leffler stability theorem and the Caputo operator property. Both of the two methods involve two steps: firstly, constructing a fractional order sliding surface; secondly, designing a single sliding control law for suppression of the nominal plant. Numerical simulations are carried out to verify the efficiency of the theoretical results.


This study was supported by a grant from the Natural Science Foundation of the Province Shandong of China (ZR2014AM006).


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