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Research Papers

Robust Finite-Time Stabilization of Fractional-Order Chaotic Systems based on Fractional Lyapunov Stability Theory

[+] Author and Article Information
Mohammad Pourmahmood Aghababa

 Electrical Engineering Department, Urmia University of Technology, P.O. Box 57155/419, Urmia, Iran e-mail: m.p.aghababa@ee.uut.ac.ir; m.pour13@gmail.com

J. Comput. Nonlinear Dynam 7(2), 021010 (Jan 09, 2012) (5 pages) doi:10.1115/1.4005323 History: Received August 11, 2011; Revised October 13, 2011; Published January 09, 2012; Online January 09, 2012

This paper concerns the problem of stabilization of uncertain fractional-order chaotic systems in finite time. On the basis of fractional Lyapunov stability theory, a robust finite-time fractional controller is introduced to control chaos of fractional-order chaotic systems in the presence of system uncertainties. The finite-time stability of the closed-loop system is analytically proved. An estimation of the convergence time is also given. Some numerical simulations are provided to illustrate the usefulness and applicability of the proposed robust finite-time control approach. It is worth noting that the proposed fractional control method is applicable for stabilizing a broad range of uncertain fractional-order nonlinear systems in a given finite time.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

The state trajectories of the uncertain fractional-order chaotic Lorenz system controlled with the proposed finite-time controller

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Figure 2

The time histories of the applied control inputs (Eq. 10) for stabilization of the uncertain fractional-order chaotic Lorenz system

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Figure 3

The state trajectories of the uncertain fractional-order hyperchaotic Chen system controlled with the proposed finite-time controller

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Figure 4

The time histories of the applied control inputs (Eq. 10) for stabilization of the uncertain fractional-order hyperchaotic Chen system

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