A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy

Bartolini, G., Ferrara, A. and Usai, E. (1998). Chattering avoidance by second order sliding mode control, IEEE Transactions on Automatic Control43(2): 241–246.10.1109/9.661074Search in Google Scholar

Bartolini, G., Ferrara, A., Usai, E. and Utkin, V. I. (2000). On multi-input chattering-free second-order sliding mode control, IEEE Transactions on Automatic Control45(5): 1711–1717.10.1109/9.880629Search in Google Scholar

Bartoszewicz, A. (1996). Remarks on ‘Discrete-time variable structure control systems’, IEEE Transactions on Industrial Electronics43(1): 235–238.Search in Google Scholar

Bartoszewicz, A. (1998). Discrete-time quasi-sliding mode control strategies, IEEE Transactions on Industrial Electronics45(4): 633–637.10.1109/41.704892Search in Google Scholar

Bartoszewicz, A. and Leśniewski, P. (2016). New switching and nonswitching type reaching laws for SMC of discrete time systems, IEEE Transactions on Control Systems Technology24(2): 670–677.10.1109/TCST.2015.2440175Search in Google Scholar

Chakrabarty, S. and Bandyopadhyay, B. (2015). A generalized reaching law for discrete time sliding mode control, Auto-matica52(1): 83–86.10.1016/j.automatica.2014.10.124Search in Google Scholar

Chakrabarty, S. and Bandyopadhyay, B. (2016). A generalized reaching law with different convergence rates, Automatica63(1): 34–37.10.1016/j.automatica.2015.10.018Search in Google Scholar

Chakrabarty, S. and Bartoszewicz, A. (2016). Improved robustness and performance of discrete time sliding mode control systems, ISA Transactions on Industrial Informatics65(1): 143–149.10.1016/j.isatra.2016.08.006Search in Google Scholar

Chang, F.J., Twu, S.H. and Chang, S. (1990). Adaptive chattering alleviation of variable structure systems, IEE Proceedings D: Control Theory and Applications137(1): 31–39.10.1049/ip-d.1990.0003Search in Google Scholar

DeCarlo, R.A., ˙Zak, S. and Matthews, G. (1988). Variable structure control of nonlinear multivariable systems: A tutorial, Proceedings of the IEEE76(3): 212–232.10.1109/5.4400Search in Google Scholar

Draženović, B. (1969). The invariance conditions in variable structure systems, Automatica5(3): 287–295.10.1016/0005-1098(69)90071-5Search in Google Scholar

Edwards, C. and Spurgeon, S. (1998). Sliding Mode Control: Theory and Applications, Taylor & Francis, London.10.1201/9781498701822Search in Google Scholar

Emelyanov, S.V. (1957). A method to obtain complex regulation laws using only the error signal or the regulated coordinate and its first derivatives, Avtomatika i Telemekhanika18(10): 873–885.Search in Google Scholar

Emelyanov, S.V. and Utkin, V.I. (1964). Stability of motion of a class of variable structure control systems, Izvestiya AN SSSR: Technical Cybernetics2(1): 140–142.Search in Google Scholar

Furuta, K. (1990). Sliding mode control of a discrete system, Systems & Control Letters14(2): 145–152.10.1016/0167-6911(90)90030-XSearch in Google Scholar

Gao, W.B., Wang, Y. and Homaifa, A. (1995). Discrete-time variable structure control systems, IEEE Transactions on Industrial Electronics42(2): 117–122.10.1109/41.370376Search in Google Scholar

Golo, G. and Milosavljević, C. (2000). Robust discrete-time chattering free sliding mode control, Systems & Control Letters41(1): 19–28.10.1016/S0167-6911(00)00033-5Search in Google Scholar

Hung, J.Y., Gao, W.B. and Hung, J.C. (1993). Variable structure control: A survey, IEEE Transactions on Industrial Electronics40(1): 2–22.10.1109/41.184817Search in Google Scholar

Itkis, U. (1976). Control Systems of Variable Structure, John Wiley&Sons, New York, NY.Search in Google Scholar

Kotta, U., Sarpturk, S.Z. and Istefanopulos, Y. (1989). Comments on ‘On the stability of discrete-time sliding mode control systems’, IEEE Transactions on Automatic Control34(9): 1021–1022.10.1109/9.35824Search in Google Scholar

Latosiński, P. (2017). Reaching law based discrete time switching quasi-sliding mode controller, Proceedings of 22nd International Conference on Methods and Models in Automation and Robotics, MMAR, Międzyzdroje, Poland, pp. 414–418.10.1109/MMAR.2017.8046863Search in Google Scholar

Latosiński, P. and Bartoszewicz, A. (2018). Discrete time sliding mode controllers with relative degree one and two switching variables, Journal of the Franklin Institute355(15): 6889–6903.10.1016/j.jfranklin.2018.07.006Search in Google Scholar

Leśniewski, P. and Bartoszewicz, A. (2015). Inverse tangent based switching type reaching law for discrete time sliding mode control systems, Proceedings of the European Control Conference, ECC’15, Linz, Austria, pp. 2390–2395.10.1109/ECC.2015.7330896Search in Google Scholar

Luis-Delgado, J.D., Al-Hadithi, B.M. and Jiménez, A. (2017). A novel method for the design of switching surfaces for discretized MIMO nonlinear systems, International Journal of Applied Mathematics and Computer Science27(1): 5–17, DOI: 10.1515/amcs-2017-0001.10.1515/amcs-2017-0001Open DOISearch in Google Scholar

Ma, H., Wu, J. and Xiong, Z. (2017). A novel exponential reaching law of discrete-time sliding-mode control, IEEE Transactions on Industrial Electronics64(5): 2245–2251.10.1109/TIE.2017.2652390Search in Google Scholar

Milosavljević, C. (1985). General conditions for the existence of a quasi-sliding mode on the switching hyperplane in discrete variable structure systems, Automation and Remote Control46(3): 307–314.Search in Google Scholar

Monsees, G. and Sherpen, J.M.A. (2001). Discrete-time sliding mode control with a disturbance estimator, Proceedings of the European Control Conference, ECC 2001, Porto, Portugal, pp. 3270–3275.10.23919/ECC.2001.7076437Search in Google Scholar

Niu, Y., Ho, D.W.C. and Wang, Z. (2010). Improved sliding mode control for discrete-time systems via reaching law, IET Proceedings on Control Theory & Applications4(11): 2245–2251.10.1049/iet-cta.2009.0296Search in Google Scholar

Qu, S., Xia, X. and Zhang, J. (2014). Dynamics of discrete-time sliding-mode-control uncertain systems with a disturbance compensator, IEEE Transactions on Industrial Electronics61(7): 3502–3510.10.1109/TIE.2013.2279369Search in Google Scholar

Ren, Y., Liu, Z., Liu, X. and Zhang, Y. (2013). A chattering free discrete-time global sliding mode controller for optoelectronic tracking system, Mathematical Problems in Engineering2013(2): 1–8.10.1155/2013/951492Search in Google Scholar

Sabanovic, A. (2011). Variable structure systems with sliding modes in motion control—a survey, IEEE Transactions on Industrial Informatics7(2): 212–223.10.1109/TII.2011.2123907Search in Google Scholar

Sarpturk, S.Z., Istefanopulos, Y. and Kaynak, O. (1987). On the stability of discrete-time sliding mode control systems, IEEE Transactions on Automatic Control22(10): 930–932.10.1109/TAC.1987.1104468Search in Google Scholar

Utkin, V.I. (1977). Variable structure systems with sliding modes, IEEE Transactions on Automatic Control22(2): 212–222.10.1109/TAC.1977.1101446Search in Google Scholar

Utkin, V.I. (1978). Sliding Modes and Their Applications in Variable Structure Systems, Mir Publishers, Moscow, pp. 212–222.10.1109/TAC.1977.1101446Search in Google Scholar

Utkin, V.I. (1984). Variable structure systems: Present and future, Automatic Remote Control44(9): 1105–1220.Search in Google Scholar

Utkin, V.I. and Drakunov, S.V. (1989). On discrete-time sliding modes, IFAC Proceedings Volumes22(3): 273–278.10.1016/S1474-6670(17)53647-2Search in Google Scholar

Veselic, B., Perunicic-Draženović, B. and Milosavljevic, C. (2010). Improved discrete-time sliding-mode position control using Euler velocity estimation, IEEE Transactions on Industrial Informatics57(11): 3840–3847.10.1109/TIE.2010.2042416Search in Google Scholar

Vivekanandan, C., Prabhakar, R. and Gnanambigai, M. (2008). A redefined quasi-sliding mode control strategy, Proceedings of World Academy of Science15(1): 292–295.Search in Google Scholar

Zhang, F. (2016). Switching reaching law based switched sliding mode control, Proceedings of the Chineese Control Conference, CCC, Chengdu, China, pp. 4735–4739.10.1109/ChiCC.2016.7554087Search in Google Scholar

Zinober, S.I., Ei-Ghezawi, O.M.E. and Billings, S.A. (1982). Multivariable variable structure adaptive model following control systems, IEE Proceedings D: Control Theory and Applications129(1): 6–12.10.1049/ip-d.1982.0002Search in Google Scholar