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Comments on “Design of sliding mode controller for a class of fractional-order chaotic systems” [Commun nonlinear sci numer simulat 17 (2012) 356-366]. (English) Zbl 1248.93037

Summary: Some comments on the paper C. Yin, S. M. Zhong, and W. F. Chen [”Design of sliding mode controller for a class of fractional-order chaotic systems”, Commun. Nonlinear Sci. Numer. Simulat. 17, 356-366 (2012, Zbl 1248.93041)] are pointed out in this note. Besides, recently developed fractional-order Lyapunov stability theorems are used to prove the finite-time occurrence of the sliding motion.

MSC:

93B12 Variable structure systems
26A33 Fractional derivatives and integrals
34A08 Fractional ordinary differential equations
37N35 Dynamical systems in control

Citations:

Zbl 1248.93041
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References:

[1] Yin, C.; Zhong, S.-M.; Chen, W.-F., Design of sliding mode controller for a class of fractional-order chaotic systems, Commun Nonlinear Sci Numer Simulat, 17, 356-366 (2012) · Zbl 1248.93041
[2] Li, Y.; Chen, Y. Q.; Podlubny, I., Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica, 45, 1965-1969 (2009) · Zbl 1185.93062
[3] Li, Y.; Chen, Y. Q.; Podlubny, I., Stability of fractional order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability, Comput Math Appl, 59, 1810-1821 (2010) · Zbl 1189.34015
[4] Utkin, V. I., Sliding modes in control optimization (1992), Springer Verlag: Springer Verlag Berlin · Zbl 0748.93044
[5] Matignon D. Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems and application multiconference, IMACS, IEEE-SMC proceedings, Lille, France; 1996. p. 963-8.; Matignon D. Stability results for fractional differential equations with applications to control processing. In: Computational engineering in systems and application multiconference, IMACS, IEEE-SMC proceedings, Lille, France; 1996. p. 963-8.
[6] Polyakov, A.; Poznyak, A., Lyapunov function design for finite-time convergence analysis: twisting controller for second-order sliding mode realization, Automatica, 45, 444-448 (2009) · Zbl 1158.93401
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