The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

Li Xiao; Junjie Bao; Xi Shi

doi:doi:10.11648/j.acm.20170602.11

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The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application

Li Xiao, Junjie Bao, Xi Shi

Published in Applied and Computational Mathematics (Volume 6, Issue 2)

Received: 31 January 2017 Accepted: 14 February 2017 Published: 6 March 2017

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Abstract

This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.

Published in	Applied and Computational Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.acm.20170602.11
Page(s)	68-74
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Nonlinear System, Exponential Stability, Unified System, Chaotic Masking

References

[1]	M. Siddique, M. Rehan, “A concept of coupled chaotic synchronous observers for nonlinear and adaptive observers-based chaos synchronization”, Nonlinear Dynamics, 2016, 84(4): 1-22.
[2]	X. Yin, Y. Ren, X. Shan. “Synchronization of discrete spatiotemporal chaos by using variable structure control,” Chaos, Solitons & Fractals, 2002, 14(7): 1077-1082.
[3]	X. Han, J. Lu, X. Wu. “Adaptive feedback synchronization of Lü system,” Chaos, Solitons & Fractals, 2004, 22(1): 221-227.
[4]	C. Tao, J. Lu, J. Lü. “The feedback synchronization of a unified chaotic system,” Acta Physica Sinica, 2002, 21(7): 1497-1501.
[5]	Z. Chen, K. Sun, T. Zhang. “Nonlinear feedback synchronization control of Liu chaotic system,” Acta Physica Sinica, 2005, 54(6): 2580-2583.
[6]	S. Nazhan, Z. Ghassemlooy K. Busawon,”Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback”, Chaos, 2016, 26(1): 013109.
[7]	S. Chen, Q. Yang, C. Wang. “Impulsive control and synchronization of unified chaotic system,” Chaos, solitons & fractals, 2004, 20(4): 751-758.
[8]	J. Sun, Y. Zhang. “Impulsive control of Rössler systems,” Physics Letters A, 2003, 306(5): 306-312.
[9]	J. Liu, S. Chen, J. Lu. “Projective synchronization in a unified chaotic system and its control,” Acta Physica Sinica, 2003, 52(7): 1595-1599.
[10]	X. Wang, Y. Wang. “Projective synchronization of autonomous chaotic system based on linear separation,” Acta Physica Sinica, 2007, 56(5): 2498-2503.
[11]	G. Wu, D. Baleanu, H. Xie, F. Chen, “Chaos synchronization of fractional chaotic maps based on the stability condition”, Physica A, 2016, 460: 374-383.
[12]	S. Yang, C. Chen, H. Yau. “Control of chaos in Lorenz systems,” Chaos, Solitons and Fractals, 2002, 13(4): 767-780.
[13]	X. Guan, Y. Tang, Z. Fan, et al. “Neural network based robust adaptive synchronization of a chaotic system,” Acta Physica Sinica, 2001, 50(11): 2112-2115.
[14]	D. Dawson, Z. Qu, J. Carroll. “On the state observation and output feedback problems for nonlinear uncertain dynamic systems,” Systems & Control Letters, 1992, 18(3): 217-222.
[15]	Z. Qu, D. Dawson. “Continuous state feedback control guaranteeing exponential stability for uncertain dynamical systems,” in Proceedings of the 30th IEEE Conference on Decision and Control, IEEE, 1991: 2636-2638.
[16]	M. Chen M, C. Wang, H. Zhang. “Chaotic Synchronization of Exponent Stability Based on Nonlinear State Observer,” International Conference on Mechatronics and Automation, IEEE, 2007: 657-662.
[17]	X. Wu, H. Wang, H. Lu. “Hyperchaotic secure communication via generalized function projective synchronization,” Nonlinear Analysis Real World Applications, 2011, 12(2): 1288-1299.
[18]	N. Li, J. Li. “Generalized projective synchronization of chaotic system based on a single driving variable and its application in secure communication,” Acta Physica Sinica, 2008, 57(10): 6093-6098.
[19]	D. Yang, H. Zhang, A. Li. “Generalized synchronization of two non-identical chaotic systems based on fuzzy model,” Acta Physica Sinica, 2007, 56(6): 3121-3126.
[20]	H. Zhang, T. Ma, J. Fu, S. Tong. “Robust lag synchronization between two different chaotic systems via dual-stage impulsive control,” Chinese Physics B, 2009, 18(9): 3751-3757.
[21]	J. Meng, X. Wang. “Phase synchronization of chaotic systems based on nonlinear observers,” Acta Physica Sinica, 2007, 56(9): 5142-5148.
[22]	H. Zhang, D. Liu, and Z. Wang. “Controlling Chaos: Suppression, Synchronization and Chaotification,” New York: Springer-Verlag, 2009, 184.
[23]	T. Ma, H. Zhang, Z. Wang. “Impulsive synchronization for unified chaotic systems with channel time-delay and parameter uncertainty,” Acta Physica Sinica, 2007, 56(7): 3796-3802.
[24]	X. Wang, X. Wu. “Chaos anti-synchronization of a class of chaotic systems based on state observer design,” Acta Physica Sinica, 2007, 56(4): 1988-1993.
[25]	X. Wang, Y. He. “Projective synchronization of the fractional order unified system,” Acta Physica Sinica, 2008, 57(3): 1485-1492.
[26]	X. Yan, D. Liu. “Control and projective synchronization of fractional-order chaotic systems based on sliding mode control,” Acta Physica Sinica, 2009, 58(6): 3747-3752.
[27]	N. Cai, Y. Jing, S. Zhang. “Adaptive synchronization and anti-synchronization of two different chaotic systems,” Acta Physica Sinica, 2009, 58(2): 802-813.
[28]	F. Jia, X. Wei, D. Lin. “Generalized synchronization of different orders of chaotic systems with unknown parameters and parameter identification,” Acta Physica Sinica, 2007, 56(10): 5640-5647.
[29]	Y. Sun, J. Ruan. “Synchronization between two different chaotic systems with noise perturbation,” Chinese Physics B, 2010, 19(7): 150-155.070513
[30]	L. Guo, Z. Xu, M. Hu. “Adaptive coupled synchronization of non-autonomous systems in ring networks,” Chinese Physics B, 2008, 17(3): 836-841.
[31]	A. Ouannas, Z. Odibat, N. shawagfeh, A. Alsaedi, A. Amad, “Universal chaos synchronization control laws for general quadratic discrete systems”, Applied Mathematical Modelling, 2017,45: 636-641.

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APA Style

Li Xiao, Junjie Bao, Xi Shi. (2017). The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Applied and Computational Mathematics, 6(2), 68-74. https://doi.org/10.11648/j.acm.20170602.11

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ACS Style

Li Xiao; Junjie Bao; Xi Shi. The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Appl. Comput. Math. 2017, 6(2), 68-74. doi: 10.11648/j.acm.20170602.11

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AMA Style

Li Xiao, Junjie Bao, Xi Shi. The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Appl Comput Math. 2017;6(2):68-74. doi: 10.11648/j.acm.20170602.11

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@article{10.11648/j.acm.20170602.11,
  author = {Li Xiao and Junjie Bao and Xi Shi},
  title = {The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {68-74},
  doi = {10.11648/j.acm.20170602.11},
  url = {https://doi.org/10.11648/j.acm.20170602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.11},
  abstract = {This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.},
 year = {2017}
}

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TY  - JOUR
T1  - The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application
AU  - Li Xiao
AU  - Junjie Bao
AU  - Xi Shi
Y1  - 2017/03/06
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170602.11
DO  - 10.11648/j.acm.20170602.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 68
EP  - 74
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170602.11
AB  - This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.
VL  - 6
IS  - 2
ER  -

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Author Information

Li Xiao

Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, PR China
Junjie Bao

Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, PR China
Xi Shi

Department of Mathematics and Information Engineering, Chongqing University of Education, Chongqing, PR China

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APA Style

Li Xiao, Junjie Bao, Xi Shi. (2017). The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Applied and Computational Mathematics, 6(2), 68-74. https://doi.org/10.11648/j.acm.20170602.11

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ACS Style

Li Xiao; Junjie Bao; Xi Shi. The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Appl. Comput. Math. 2017, 6(2), 68-74. doi: 10.11648/j.acm.20170602.11

Copy | Download

AMA Style

Li Xiao, Junjie Bao, Xi Shi. The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application. Appl Comput Math. 2017;6(2):68-74. doi: 10.11648/j.acm.20170602.11

Copy | Download

@article{10.11648/j.acm.20170602.11,
  author = {Li Xiao and Junjie Bao and Xi Shi},
  title = {The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application},
  journal = {Applied and Computational Mathematics},
  volume = {6},
  number = {2},
  pages = {68-74},
  doi = {10.11648/j.acm.20170602.11},
  url = {https://doi.org/10.11648/j.acm.20170602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170602.11},
  abstract = {This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - The Global Exponential Stability Analysis of Nonlinear Dynamic System and Application
AU  - Li Xiao
AU  - Junjie Bao
AU  - Xi Shi
Y1  - 2017/03/06
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.20170602.11
DO  - 10.11648/j.acm.20170602.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 68
EP  - 74
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20170602.11
AB  - This paper studies the global exponential stability for a class of nonlinear dynamical systems. A new state feedback controller is designed, which can effectively stabilize this kind of nonlinear system to the equilibrium point at exponential rate. The feasibility of the method is proved theoretically, and an algorithm is systematically proposed to configure the related parameters of the controller. Then simulation results show the effectiveness of the proposed control method.
VL  - 6
IS  - 2
ER  -

Copy | Download