IEEE/CAA Journal of Automatica Sinica
Citation: | R. Zhang, S. Yang, and S. Feng, “Stability analysis of a class of nonlinear fractional differential systems with Riemann-Liouville derivative,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 8, pp. 1883–1885, Aug. 2024. doi: 10.1109/JAS.2016.7510199 |
[1] |
J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Commun. Nonlinear. Sci. Numer. Simul., vol. 16, pp. 1140–1153, 2011.
|
[2] |
D. Matignon, “Stability results for fractional di? Erential equations with applications to control processing,” in Proc. IMACS-SMC, 1996, vo. 2, pp. 963–968.
|
[3] |
W. Deng, C. Li, and Q. Guo, “Analysis of fractional differential equations with multi-orders,” Fractals, vol. 15, pp. 173–182, 2007.
|
[4] |
W. Deng, C. Li, and J. Lu, “Stability analysis of linear fractional differential system with multiple time delays,” Nonlinear Dynamics, vol. 48, pp. 409–416, 2007.
|
[5] |
M. Moze, J. Sabatier, amd A. Oustaloup. “LMI characterization of fractional systems stability,” in Advances in Fractional Calculus. Dordrecht, The Netherlands: Springer, 2007, pp. 419–434.
|
[6] |
Y. Li, Y. Chen, and I. Podlubny, “Mittag-Leffler stability of fractional order nonlinear dynamic systems,” Automatica, vol. 45, pp. 1965–1969, 2009.
|
[7] |
Y. Li, Y. Chen, and I. Podlubny, “Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability,” Comput. & Math. Applica., vol. 59, pp. 1810–1821, 2010.
|
[8] |
X. Wen, Z. Wu, and J. Lu, “Stability analysis of a class of nonlinear fractional-order systems,” IEEE Trans. Circuits and Systems II, vol. 55, pp. 1178–1182, 2008.
|
[9] |
X. Zhou, L. Hu, S. Liu, and W. Jiang, “Stability criterion for a class of nonlinear fractional differential system,” Appl. Math. Lett., vol. 28, pp. 25–29, 2014.
|
[10] |
R. Zhang and S. Yang, “Stabilization of fractional-order chaotic system via a single state adaptive-feedback controller,” Nonlinear Dyn., vol. 68, pp. 45–51, 2012.
|
[11] |
M. Faieghi, S. Kuntanapreeda, H. Delavari, and D. Baleanu, “LMI-based stabilization of a class of fractional-order chaotic systems,” Nonlinear Dyn., vol.72, pp. 301–309, 2013.
|
[12] |
J. Wang and X. Li, “Ulam-Hyers stability of fractional Langevin equations,” Applied Math. and Comput., vol. 258, pp. 72–83, 2015.
|
[13] |
J. Wang and Y. Zhang, “Ulam-Hyers-Mittag-Leffler stability of fractional-order delay differential equations,” Optimization, vol. 63, no. 8, pp. 1181–1190, 2014.
|
[14] |
R. Zhang, G. Tian, S. Yang, and H. Cao, “Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2),” ISA Trans., vol. 56, pp. 102–110, 2015.
|
[15] |
I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Phys. Rev. Lett., vol. 91, p. 34101, 2003.
|
[16] |
C. Li and G. Chen, “Chaos in the fractional order Chen system and its control,” Chaos Solitons Fractals, vol. 22, pp. 549–554, 2004.
|
[17] |
J. Lu, “Chaotic dynamics of the fractional-order Lu system and its synchronization,” Phys. Lett. A, vol. 354, pp. 305–311, 2006.
|
[18] |
X. Wang and M. Wang, “Dynamic analysis of the fractional-order Liu system and its synchronization,” Chaos Solitons Fractals, vol. 17, p. 33106, 2007.
|
[19] |
J. Lu, “Chaotic dynamics and synchronization of fractional-order Arneado’s systems,” Chaos Solitons Fractals, vol. 26, pp. 1125–1133, 2005.
|
[20] |
T. Hartly, C. Lorenzo, and H. K. Qammer, “Chaos in a fractional order Chua’s system,” IEEE Trans. CAS: I, vol. 42, pp. 485–490, 1995.
|
[21] |
A. Hegazi and A. Matouk, “Dynamical behaviors and synchronization in the fractional order hyperchaotic Chen system,” Appl. Math. Lett., vol. 24, pp. 1938–1944, 2011.
|
[22] |
F. Wang, Y. Yang, amd M. Hu, “Asymptotic stability of delayed fractional-order neural networks with impulsive effects,” Neurocomputing, vol. 154, pp. 239–244, 2015.
|