Page 623 - Mathematical Techniques of Fractional Order Systems

Control and Synchronization Chapter | 19 593

Soliman, N.S., Said, L.A., Azar, A.T., Madian, A.H., Radwan, A.G., Ouannas, A., 2017.
Fractional Controllable Multi-Scroll V-Shape Attractor with Parameters Effect. The 6th
International Conference on Modern Circuits and Systems Technologies (MOCAST), 4-6
May 2017, Thessaloniki Greece.
Srivastava, H.M., Owa, S., 1989. Univalent Functions, Fractional Calculus, and Their
Applications. Halsted Press, Ellis Horwood; New York; Toronto.
Stenflo, L., 1996. Generalized Lorenz equations for acoustic-gravity waves in the atmosphere.
Phys. Scripta 53 (1), 83 84.
Strogatz, S.H., 2014. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology,
Chemistry, and Engineering. Westview Press, Boulder, CO.
Tabari, M.Y., Kamyad, A.V., 2013. Design optimal fractional PID controller for inverted pendu-
lum with genetic algorithm. Int. J. Sci. Eng. Res. 4 (2), 2 5.
Tavazoei, M.S., Haeri, M., 2007. A necessary condition for double scroll attractor existence in
fractional-order systems. Phys. Lett. A 367, 102 113.
Tavazoei, M.S., Haeri, M., 2008. Chaotic attractors in incommensurate fractional order systems.
Phys. D Nonlinear Phenom. 237 (20), 2628 2637.
Tenreiro Machado, J.A., Silva, M.F., Barbosa, R.S., Jesus, I.S., Reis, C.M., Marcos, M.G., et al.,
2010. Some applications of fractional calculus in engineering. Math. Probl. Eng. 2010.
Available from: https://doi.org/10.1155/2010/639801, Article ID 639801, 34 pages.
Tolba, M.F., AbdelAty, A.M., Soliman, N.S., Said, L.A., Madian, A.H., Azar, A.T., et al., 2017.
FPGA implementation of two fractional order chaotic systems. Int. J. Electr. Commun. 28
(2017), 162 172.
Tseng, C.-C., 2007. Design of FIR and IIR fractional order Simpson digital integrators. Signal
Processing 87 (5), 1045 1057.
Vaidyanathan, S., Azar, A.T., 2015a. Anti-synchronization of identical chaotic systems using
sliding mode control and an application to Vaidyanathan-Madhavan Chaotic Systems.
In: Azar, A.T., Zhu, Q. (Eds.), Advances and Applications in Sliding Mode Control systems,
Studies in Computational Intelligence book Series, Vol. 576. Springer-Verlag GmbH Berlin,
Heidelberg, pp. 527 547. Available from: http://dx.doi.org/10.1007/978-3-319-11173-5_19.
Vaidyanathan, S., Azar, A.T., 2015b. Hybrid synchronization of identical chaotic systems using
sliding mode control and an application to Vaidyanathan Chaotic Systems. In: Azar, A.T.,
Zhu, Q. (Eds.), Advances and Applications in Sliding Mode Control systems, Studies in
Computational Intelligence book Series, Vol. 576. Springer-Verlag GmbH Berlin,
Heidelberg, pp. 549 569. Available from: http://dx.doi.org/10.1007/978-3-319-11173-5_20.
Vaidyanathan, S., Azar, A.T., 2015c. Analysis, control and synchronization of a nine-term 3-D novel
chaotic system. In: Azar, A.T., Vaidyanathan, S. (Eds.), Chaos Modeling and Control Systems
Design, Studies in Computational Intelligence, Vol. 581. Springer-Verlag GmbH Berlin,
Heidelberg, pp. 3 17. Available from: http://dx.doi.org/10.1007/978-3-319-13132-0_1.
Vaidyanathan, S., Azar, A.T., 2015d. Analysis and control of a 4-D novel hyperchaotic system.
In: Azar, A.T., Vaidyanathan, S. (Eds.), Chaos Modeling and Control Systems Design,
Studies in Computational Intelligence, Vol. 581. Springer-Verlag GmbH Berlin, Heidelberg,
pp. 19 38. Available from: http://dx.doi.org/10.1007/978-3-319-13132-0_2.
Vaidyanathan, S., Azar, A.T., 2016a. Takagi-Sugeno Fuzzy Logic Controller for Liu-Chen Four-
Scroll Chaotic System. Int. J. Intel. Eng. Inf. 4 (2), 135 150.
Vaidyanathan, S., Azar, A.T., 2016b. Dynamic analysis, adaptive feedback control and synchro-
nization of an eight-term 3-D novel chaotic system with three quadratic nonlinearities,
Studies in Fuzziness and Soft Computing, Vol. 337. Springer-Verlag, Germany,
pp. 155 178.