Sliding mode control of uncertain fractional order systems with delay

References

• Asl, F. M., & Ulsoy, A. G. (2003). Analysis of a system of linear delay differential equations. ASME Journal of Dynamic Systems, Measurement, and Control, 125(2), 215–223. doi: 10.1115/1.1568121
   Web of Science ®Google Scholar
• Bandyopadhyay, B., & Kamal, S. (2015). Sliding mode control of fractional order systems. Stabilization and control of fractional order systems: A sliding mode approach (pp. 91–114). Cham: Springer International Publishing.
   Google Scholar
• Calderon, A. J., Vinagre, B. M., & Feliu, V. (2006). Fractional order control strategies for power electronic buck converters. Signal Processing, 86, 2803–2819. doi: 10.1016/j.sigpro.2006.02.022
   Web of Science ®Google Scholar
• Chen, Y., & Moore, K. (2002). Analytical stability bound for a class of delayed fractional-order dynamic systems. Nonlinear Dynamics, 29(1–4), 191–200. doi: 10.1023/A:1016591006562
   Web of Science ®Google Scholar
• Choi, H. H. (2007). LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems. IEEE Transactions on Automatic Control, 52(4), 736–742. doi: 10.1109/TAC.2007.894543
   Web of Science ®Google Scholar
• Choudhary, N., Kar, I. N., & Sivaramakrishnan, J. (2015). A direct method for stabilization of time delay systems. 2015 Annual IEEE India conference (INDICON) (pp. 1–6).
   Google Scholar
• Choudhary, N., Sivaramakrishnan, J., & Kar, I. N. (2017). Analysis of multidimensional time delay systems using Lambert W function. ASME Journal of Dynamic Systems, Measurement, and Control, 139(11), 114506–6. doi: 10.1115/1.4036874
   Web of Science ®Google Scholar
• Deng, W., & Li, C. (2005). Synchronization of chaotic fractional Chen system. Journal of the Physical Society of Japan, 74(6), 1645–1648. doi: 10.1143/JPSJ.74.1645
   Web of Science ®Google Scholar
• Deng, W., Li, C., & Lu, J. (2007). Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dynamics, 48, 409–416. doi: 10.1007/s11071-006-9094-0
   Web of Science ®Google Scholar
• Djennoune, S., & Bettayeb, M. (2013). Optimal synergetic control for fractional-order systems. Automatica, 49(7), 2243–2249. doi: 10.1016/j.automatica.2013.04.007
   Web of Science ®Google Scholar
• Edwards, C., & Spurgeon, S. (1998). Sliding mode control: Theory and applications. London: Taylor & Francis.
   Google Scholar
• Efe, M. O. (2010). Fractional order sliding mode controller design for fractional order dynamic systems. New trends in nanotechnology and fractional calculus applications (pp. 463–470).
   Google Scholar
• El-Khazali, R., & Ahmad, W. (2006). Variable structure control of fractional time delay systems, Porto, Portugal, 4–6 June.
   Google Scholar
• El-Khazali, R., Ahmad, W., & Al-Assaf, Y. (2006). Sliding mode control of generalized fractional chaotic systems. International Journal of Bifurcations and Chaos, 16(10), 3113–3152. doi: 10.1142/S0218127406016719
   Web of Science ®Google Scholar
• Farges, C., Moze, M., & Sabatier, J. (2010). Pseudo-state feedback stabilization of commensurate fractional order systems. Automatica, 46(10), 1730–1734. doi: 10.1016/j.automatica.2010.06.038
   Web of Science ®Google Scholar
• Ghosh, S., Folly, K., & Patel, A. (2017). Synchronized versus non-synchronized feedback for speed-based wide-area PSS: Effect of time-delay. IEEE Transactions on Smart Grid, PP(99), 1–10.
   Google Scholar
• Hartley, T. T., & Lorenzo, C. F. (2002). Dynamics and control of initialized fractional-order systems. Nonlinear Dynamics, 29(1), 201–233. doi: 10.1023/A:1016534921583
   Web of Science ®Google Scholar
• Hung, J. Y., Gao, W., & Hung, J. C. (1993). Variable structure control: A survey. IEEE Transactions on Industrial Electronics, 40(1), 2–22. doi: 10.1109/41.184817
   Web of Science ®Google Scholar
• Hwang, C., & Cheng, Y.-C. (2005). A note on the use of the Lambert W function in the stability analysis of time-delay systems. Automatica, 41(11), 1979–1985. doi: 10.1016/j.automatica.2005.05.020
   Web of Science ®Google Scholar
• Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of fractional differential equations (North-Holland Mathematics Studies)(Vol. 204). New York: Elsevier Science Inc.
   Google Scholar
• Li, C., Deng, W., & Xu, D. (2006). Chaos synchronization of the Chua system with a fractional order. Physica A: Statistical Mechanics and its Applications, 360(2), 171–185. doi: 10.1016/j.physa.2005.06.078
   Web of Science ®Google Scholar
• Lu, J. G. (2006). Synchronization of a class of fractional-order chaotic systems via a scalar transmitted signal. Chaos, Solitons and Fractals, 27(2), 519–525. doi: 10.1016/j.chaos.2005.04.032
   Web of Science ®Google Scholar
• Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing. Computational engineering in systems applications (pp. 963–968).
   Google Scholar
• Monje, C., Chen, Y., Vinagre, B., Xue, D., & Feliu-Batlle, V. (2010). Fractional order systems and controls: Fundamentals and applications. London: Springer.
   Google Scholar
• Oldham, K. B., & Spanier, J (1974). The fractional calculus. New York, NY: Academic Press.
   Google Scholar
• Pisano, A., Rapai, M. R., Jelii, Z. D., & Usai, E. (2010). On second-order sliding-mode control of fractional-order dynamics. Proceedings of the 2010 American control conference (pp. 6680–6685).
   Google Scholar
• Podlubny, I. (1999b). Fractional-order systems and piλdμ controllers. IEEE Transactions on Automatic Control, 44(1), 208–213. doi: 10.1109/9.739144
   Web of Science ®Google Scholar
• Podlubny, I (1999a). Fractional differential equations. San Diego: Academic Press.
   Google Scholar
• Richard, J. P., Gouaisbaut, F., & Perruquetti, W. (2001). Sliding mode control in the presence of delay. Kybernetika, 37, 277–294.
   Web of Science ®Google Scholar
• Sabatier, J., Farges, C., & Trigeassou, J.-C. (2014). Fractional systems state space description: Some wrong ideas and proposed solutions. Journal of Vibration and Control, 20(7), 1076–1084. doi: 10.1177/1077546313481839
   Web of Science ®Google Scholar
• Si-Ammour, A., Djennoune, S., & Bettayeb, M. (2009). A sliding mode control for linear fractional systems with input and state delays. Communications in Nonlinear Science & Numerical Simulation, 14(5), 2310–2318. doi: 10.1016/j.cnsns.2008.05.011
   Web of Science ®Google Scholar
• Sierociuk, D., Skovranek, T., Macias, M., Podlubny, I., Petras, I., Dzielinski, A., & Ziubinski, P. (2015). Diffusion process modeling by using fractional-order models. Applied Mathematics and Computation, 257, 2–11. doi: 10.1016/j.amc.2014.11.028
   Web of Science ®Google Scholar
• Tavazoei, M. S., & Haeri, M. (2008). Synchronization of chaotic fractional order systems via active sliding mode controller. Physica A, 378(1), 57–70. doi: 10.1016/j.physa.2007.08.039
   Web of Science ®Google Scholar
• Tepljakov, A., Petlenkov, E., & Belikov, J. (2011). Fomcon: Fractional-order modeling and control toolbox for Matlab. Proceedings of the 18th international conference mixed design of integrated circuits and systems – MIXDES 2011 (pp. 684–689).
   Google Scholar
• Trigeassou, J., Maamri, N., Sabatier J., & Oustaloup, A. (2012). State variables and transients of fractional order differential systems. Computers & Mathematics with Applications, 64(10), 3117–3140. doi: 10.1016/j.camwa.2012.03.099
   Web of Science ®Google Scholar
• Valerio, D. (2012). Introducing fractional sliding mode control, Porto.
   Google Scholar
• Yi, S., Nelson, P. W., & Ulsoy, A. G. (2010). Time-delay systems: Analysis and control using the Lambert W function. Singapore: World Scientific.
   Google Scholar
• Yin, C., Cheng, Y., Chen Y., Stark, B., & Zhong, S. (2015). Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems. Nonlinear Dynamics, 82(1), 39–52. doi: 10.1007/s11071-015-2136-8
   Web of Science ®Google Scholar
• Yin, C., Cheng, Y., Zhong, S., & Bai, Z. (2016). Fractional-order switching type control law design for adaptive sliding mode technique of 3D fractional-order nonlinear systems. Complexity, 21(6), 363–373. doi: 10.1002/cplx.21696
   Web of Science ®Google Scholar
• Yin, C., Huang, X., Chen, Y., Dadras, S., Zhong, S., & Cheng, Y. (2017). Fractional-order exponential switching technique to enhance sliding mode control. Applied Mathematical Modelling, 44, 705–726. doi: 10.1016/j.apm.2017.02.034
   Web of Science ®Google Scholar
• Yousefi, M., & Binazadeh, T. (2018). Delay-independent sliding mode control of time-delay linear fractional order systems. Transactions of the Institute of Measurement and Control, 40(4), 1212–1222. doi: 10.1177/0142331216678059
   Web of Science ®Google Scholar
• Zhou, T., & Li, C. (2005). Synchronization in fractional-order differential systems. Physica D: Nonlinear Phenomena, 212(1-2), 111–125. doi: 10.1016/j.physd.2005.09.012
   Web of Science ®Google Scholar