Stabilization of fractional order unified chaotic systems via linear state feedback controller

E. G. Razmjou; A. Ranjbar; Z. Rahmani; R. Ghaderi; S. Momani

doi:10.1007/978-1-4614-0457-6_7

Stabilization of fractional order unified chaotic systems via linear state feedback controller

E. G. Razmjou
, A. Ranjbar
, Z. Rahmani
, R. Ghaderi
, S. Momani

Babol Noshirvani University of Technology
University of Jordan

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

Abstract

This chapter deals with an asymptotical stability of the fractional-order unified chaotic systems. A unified system is presented to show that three chaotic dynamics of the Lorenz, the Chen, and the Lü systems are in the same structure. Dynamics of the Lorenz, the Chen, and the Lü are categorized in a unified system with a same structure. This system will be distinguished different when an only relevant parameter a is accordingly tuned. A systematic linear state feedback controller is gained to stabilize these systems. This controller will be shown increasing the stability region with respect to their integer order counterpart. The stability region will be accordingly increased with respect to their integer order alternative. Simulation results are demonstrated for the Chen and the Lü fractional-order systems to illustrate the effectiveness of the proposed control scheme.

Original language	English
Title of host publication	Fractional Dynamics and Control
Publisher	Springer New York
Pages	85-94
Number of pages	10
ISBN (Electronic)	9781461404576
ISBN (Print)	9781461404569
DOIs	https://doi.org/10.1007/978-1-4614-0457-6_7
State	Published - 1 Jan 2012
Externally published	Yes

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Cite this

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title = "Stabilization of fractional order unified chaotic systems via linear state feedback controller",

abstract = "This chapter deals with an asymptotical stability of the fractional-order unified chaotic systems. A unified system is presented to show that three chaotic dynamics of the Lorenz, the Chen, and the L{\"u} systems are in the same structure. Dynamics of the Lorenz, the Chen, and the L{\"u} are categorized in a unified system with a same structure. This system will be distinguished different when an only relevant parameter a is accordingly tuned. A systematic linear state feedback controller is gained to stabilize these systems. This controller will be shown increasing the stability region with respect to their integer order counterpart. The stability region will be accordingly increased with respect to their integer order alternative. Simulation results are demonstrated for the Chen and the L{\"u} fractional-order systems to illustrate the effectiveness of the proposed control scheme.",

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AU - Razmjou, E. G.

AU - Ranjbar, A.

AU - Rahmani, Z.

AU - Ghaderi, R.

AU - Momani, S.

PY - 2012/1/1

Y1 - 2012/1/1

N2 - This chapter deals with an asymptotical stability of the fractional-order unified chaotic systems. A unified system is presented to show that three chaotic dynamics of the Lorenz, the Chen, and the Lü systems are in the same structure. Dynamics of the Lorenz, the Chen, and the Lü are categorized in a unified system with a same structure. This system will be distinguished different when an only relevant parameter a is accordingly tuned. A systematic linear state feedback controller is gained to stabilize these systems. This controller will be shown increasing the stability region with respect to their integer order counterpart. The stability region will be accordingly increased with respect to their integer order alternative. Simulation results are demonstrated for the Chen and the Lü fractional-order systems to illustrate the effectiveness of the proposed control scheme.

AB - This chapter deals with an asymptotical stability of the fractional-order unified chaotic systems. A unified system is presented to show that three chaotic dynamics of the Lorenz, the Chen, and the Lü systems are in the same structure. Dynamics of the Lorenz, the Chen, and the Lü are categorized in a unified system with a same structure. This system will be distinguished different when an only relevant parameter a is accordingly tuned. A systematic linear state feedback controller is gained to stabilize these systems. This controller will be shown increasing the stability region with respect to their integer order counterpart. The stability region will be accordingly increased with respect to their integer order alternative. Simulation results are demonstrated for the Chen and the Lü fractional-order systems to illustrate the effectiveness of the proposed control scheme.

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EP - 94

BT - Fractional Dynamics and Control

PB - Springer New York

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Stabilization of fractional order unified chaotic systems via linear state feedback controller

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