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Research Papers

A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems With One Control Input

[+] Author and Article Information
Pitcha Khamsuwan

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

Suwat Kuntanapreeda

Department of Mechanical and
Aerospace Engineering,
Faculty of Engineering,
King Mongkut's University of
Technology North Bangkok,
Bangkok 10800, Thailand
e-mails: suwat@kmutnb.ac.th;
suwatkd@gmail.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 12, 2015; final manuscript received April 5, 2016; published online May 24, 2016. Assoc. Editor: Dumitru Baleanu.

J. Comput. Nonlinear Dynam 11(5), 051021 (May 24, 2016) (7 pages) Paper No: CND-15-1368; doi: 10.1115/1.4033384 History: Received November 12, 2015; Revised April 05, 2016

This paper focuses on stabilization of fractional-order unified chaotic systems. In contrast to existing methods in literature, the proposed method requires only the system output for feedback and uses only one control input. The controller consists of a state feedback control law and a dynamic estimator. Sufficient stability conditions are derived using a fractional-order extension of the Lyapunov direct method and a new lemma of the Caputo fractional derivative. The conditions are expressed in the form of linear matrix inequalities (LMIs). All the parameters of the controller can be simultaneously obtained by solving the LMIs. Numerical simulations are provided to illustrate the feasibility and effectiveness of the proposed method.

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References

Figures

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Fig. 1

Uncontrolled fractional-order Lorenz system (α=0 and q=0.98). The initial condition x(0)=[1, 2, 3]T. (a) State response and (b) chaotic attractor.

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Fig. 2

Uncontrolled fractional-order Chen system (α=1 and q=0.80). The initial condition x(0)=[1, 2, 3]T. (a) State response and (b) chaotic attractor.

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Fig. 3

Uncontrolled fractional-order Lü system (α=0.8 and q=0.90). The initial condition x(0)=[1, 2, 3]T. (a) State response and (b) chaotic attractor.

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Fig. 4

Response of the controlled fractional-order Lorenz system

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Fig. 5

Phase-space trajectory of the controlled fractional-order Lorenz system

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Fig. 6

Estimation errors and control input of the controlled fractional-order Lorenz systems

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Fig. 7

Response of the controlled fractional-order Chen system

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Fig. 8

Phase-space trajectory of the controlled fractional-order Chen system

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Fig. 9

Estimation errors and control input of the controlled fractional-order Chen systems

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Fig. 10

Response of the controlled fractional-order Lü system

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Fig. 11

Phase-space trajectory of the controlled fractional-order Lü system

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Fig. 12

Estimation errors and control input of the controlled fractional-order Lü systems

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