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Chaos Synchronization of Fractional-Order Chaotic Systems With Input Saturation

[+] Author and Article Information
Pitcha Khamsuwan, Teerawat Sangpet, Suwat Kuntanapreeda

Department of Mechanical
and Aerospace Engineering,
Faculty of Engineering,
King Mongkut's University
of Technology North Bangkok,
Bangkok 10800, Thailand

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 13, 2017; final manuscript received March 11, 2018; published online July 26, 2018. Assoc. Editor: Themistoklis Sapsis.

J. Comput. Nonlinear Dynam 13(9), 090903 (Jul 26, 2018) (8 pages) Paper No: CND-17-1264; doi: 10.1115/1.4039681 History: Received June 13, 2017; Revised March 11, 2018

This paper deals with the problem of master-slave synchronization of fractional-order chaotic systems with input saturation. Sufficient stability conditions for achieving the synchronization are derived from the basis of a fractional-order extension of the Lyapunov direct method, a new lemma of the Caputo fractional derivative, and a local sector condition. The stability conditions are formulated in linear matrix inequality (LMI) forms and therefore are readily solved. The fractional-order chaotic Lorenz and hyperchaotic Lü systems with input saturation are utilized as illustrative examples. The feasibility of the proposed synchronization scheme is demonstrated through numerical simulations.

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Figures

Grahic Jump Location
Fig. 2

Uncontrolled fractional-order hyperchaotic Lü system (q = 0.95)

Grahic Jump Location
Fig. 1

Uncontrolled fractional-order chaotic Lorenz system (q = 0.98)

Grahic Jump Location
Fig. 3

System responses of the fractional-order chaotic Lorenz systems

Grahic Jump Location
Fig. 4

Synchronization errors of the fractional-order chaotic Lorenz systems

Grahic Jump Location
Fig. 5

Control signal of the fractional-order chaotic Lorenz systems

Grahic Jump Location
Fig. 8

Control signals of the fractional-order hyperchaotic Lü systems

Grahic Jump Location
Fig. 6

System responses of the fractional-order hyperchaotic Lü systems

Grahic Jump Location
Fig. 7

Synchronization errors of the fractional-order hyperchaotic Lü systems

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