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Response to the comments on “Design of sliding mode controller for a class of fractional-order chaotic systems”. (English) Zbl 1261.93030
Summary: This paper is a response to the comments on the paper of M. P. Aghababa [“Comments on ‘Design of sliding mode controller for a class of fractional-order chaotic systems’”, ibid. 17, No. 3, 1485–1488 (2012; Zbl 1248.93037)]. The following scripts are to address and discuss the comments.

MSC:
93B12 Variable structure systems
34A08 Fractional ordinary differential equations and fractional differential inclusions
37N35 Dynamical systems in control
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[1] Aghababa, M.P., Comments on “design of sliding mode controller for a class of fractional-order chaotic systems”, Commun nonlinear sci numer simul, 17, 1485-1488, (2012) · Zbl 1248.93037
[2] 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 simul, 17, 356-366, (2012) · Zbl 1248.93041
[3] Aghababa, M.P., Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller, Commun nonlinear sci numer simul, 17, 2670-2681, (2012) · Zbl 1248.93146
[4] Aghababa MP. Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonlinear Dynam. doi: http://dx.doi.org/10.1007/s11071-011-0261-6. · Zbl 1253.93016
[5] Pourmahmood, M.; Khanmohammadi, S.; Alizadeh, G., Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller, Commun nonlinear sci numer simul, 16, 2853-2868, (2011) · Zbl 1221.93131
[6] Aghababa, M.P.; Khanmohammadi, S.; Alizadeh, G., Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique, Appl math model, 35, 3080-3091, (2011) · Zbl 1219.93023
[7] Zhang, R.; Yang, S., Adaptive synchronization of fractional-order chaotic systems via a single driving variable, Nonlinear dynam, 66, 831-837, (2011) · Zbl 1242.93030
[8] Razmjou EG, Ranjbar A, Rahmani Z, Ghaderi R. Robust synchronization and parameter identification of fractional-order unified chaotic system. In: Third conference on nonlinear science and complexity, Ankara, Turkey; 2010.
[9] Si-Ammour, A.; Djennoune, S.; Bettaye, M., A sliding mode control for linear fractional system with input and state delays, Commun nonlinear sci numer simul, 14, 2310-2318, (2009) · Zbl 1221.93048
[10] Balochian, S.; Sedigh, A.K.; Zare, A., Stabilization of multi-input hybrid fractional-order systems with state delay, ISA trans, 50, 21-27, (2011)
[11] Dadras, S.; Momeni, H.R., Control of a fractional-order economical system via sliding mode, Physica A, 389, 2434-2442, (2010)
[12] Aghababa, M.P., Comments on adaptive synchronization of fractional-order chaotic systems via a single driving variable, Nonlinear dynam, 66, 839-842, (2011) · Zbl 1243.93022
[13] Zhang, R.; Yang, S., Response to the comments on adaptive synchronization of fractional-order chaotic systems via a single driving variable, Nonlinear dynam, 66, 843-844, (2011) · Zbl 1242.93097
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