A Novel Method for the Design of Switching Surfaces for Discretized MIMO Nonlinear Systems

Ababneh, M., Salah, M. and Alwidyanm, K. (2011). Linearization of nonlinear dynamical systems: A comparative study, Jordan Journal of Mechanical and Industrial Engineering5(6): 567–571.Search in Google Scholar

Ackermann, J. and Utkin, V. (1994). Sliding mode control design based on Ackermann’s formula, Proceedings of the 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, USA, Vol. 4, pp. 3622–3627.Search in Google Scholar

Åström, K.J. and Wittenmark, B. (1997). Computer-Controlled Systems. Theory and Design, 3rd Edn., Prentice-Hall, Upper Saddle River, NJ.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. (2014). An optimal sliding mode congestion controller for connection-oriented communication networks with lossy links, International Journal of Applied Mathematics and Computer Science24(1): 87–97, DOI: 10.2478/amcs-2014-0007.10.2478/amcs-2014-0007Search in Google Scholar

Camacho, O. and Smith, C.A. (2000). Sliding mode control: An approach to regulate nonlinear chemical processes, ISA Transactions39(2): 205–218.10.1016/S0019-0578(99)00043-9Search in Google Scholar

Choi, H.H. (2003). An LMI-based switching surface design method for a class of mismatched uncertain systems, IEEE Transactions on Automatic Control48(9): 1634–1638.10.1109/TAC.2003.817007Search in Google Scholar

DeCarlo, R., 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

Dorling, C. and Zinober, A. (1986). Two approaches to hyperplane design in multivariable structure control systems, International Journal of Control44(1): 65–82.10.1080/00207178608933583Search in Google Scholar

Draženović, B., Milosavljević, Č. and Veselić, B. (2013). Comprehensive approach to sliding mode design and analysis in linear systems, in B. Bandyopdhyay et al. (Eds.), Advances in Sliding Mode Control: Concept, Theory and Implementation, Springer, Heidelberg, pp. 1–19.10.1007/978-3-642-36986-5_1Search in Google Scholar

Edwards, C. and Spurgeon, S. (2003). Linear matrix inequality methods for designing sliding mode output feedback controllers, IEE Proceedings: Control Theory and Applications150(5): 539–545.10.1049/ip-cta:20030707Search in Google Scholar

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

Furuta, K. and Pan, Y. (1995). A new approach to design a sliding sector for VSS controller, Proceedings of the 1995 American Control Conference, Seatle, WA, USA, Vol. 2, pp. 1304–1308.Search in Google Scholar

Furuta, K. and Pan, Y. (2002). Discrete-time variable structure control, in X. Yu and J.-X. Xu (Eds.), Variable Structure Systems: Towards the 21st Century, Springer, Berlin, pp. 57–81.10.1007/3-540-45666-X_3Search in Google Scholar

Gao, W. and Hung, J. (1993). Variable structure control of nonlinear systems: A new approach, IEEE Transactions on Industrial Electronics40(1): 45–55.10.1109/41.184820Search in Google Scholar

Gao, W., 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

Gatzke, E.P., Meadows, E.S., Wang, C. and Doyle, F.J. (2000). Model based control of a four-tank system, Computers & Chemical Engineering24(2): 1503–1509.10.1016/S0098-1354(00)00555-XSearch in Google Scholar

Ghaffari, A. and Yazdanpanah, M. (2008). Nonlinear sliding surfaces: Computing and existence of solution, International Conference on Control, Automation and Systems, ICCAS 2008, Seoul, Korea, pp. 1610–1615.Search in Google Scholar

Hung, J.Y., Gao, W. 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

Johansson, K. and Nunes, J. (1998). A multivariable laboratory process with an adjustable zero, Proceedings of the 1998 American Control Conference, Philadelphia, PA, USA, Vol. 4, pp. 2045–2049.Search in Google Scholar

Kim, K.-S., Park, Y. and Oh, S.-H. (2000). Designing robust sliding hyperplanes for parametric uncertain systems: A Riccati approach, Automatica36(7): 1041–1048.10.1016/S0005-1098(00)00014-5Search in Google Scholar

Lin, Y., Shi, Y. and Burton, R. (2013). Modeling and robust discrete-time sliding-mode control design for a fluid power electrohydraulic actuator (EHA) system, IEEE/ASME Transactions on Mechatronics18(1): 1–10.10.1109/TMECH.2011.2160959Search in Google Scholar

Milosavljević, Č. (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

Mondal, S., Gokul, T. and Mahanta, C. (2012). Chattering free sliding mode controller for mismatched uncertain system, 7th IEEE International Conference on Industrial and Information Systems (ICIIS), Chennal, India, pp. 1–6.Search in Google Scholar

Nadzinski, G., Vladev, G. and Zheng, Y. (2012). A design of discrete-time SMC for nonlinear systems based on fuzzy T–S model, 6th IEEE International Conference on Intelligent Systems (IS), Sofia, Bulgaria, pp. 317–324.Search in Google Scholar

Pai, M.-C. (2008). Discrete-time output feedback sliding mode control for uncertain systems, Journal of Marine Science and Technology16(4): 295–300.10.51400/2709-6998.2016Search in Google Scholar

Perruquetti, W. and Barbot, J.-P. (2002). Sliding Mode Control in Engineering, Marcel Dekker, New York, NY.10.1201/9780203910856Search in Google Scholar

Potts, R. and Yu, X. (1991). Discrete variable structure system with pseudo-sliding mode, Journal of the Australian Mathematical Society B: Applied Mathematics32(04): 365–376.10.1017/S0334270000008481Search 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

Rui, D. and Dong-wei, S. (2011). Optimal sliding mode design for nonlinear discrete-time systems, 30th Chinese Control Conference (CCC), Yantai, China, pp. 738–742.Search in Google Scholar

Sira-Ramírez, H. (1986). Variable structure control of nonlinear systems through simplified uncertain models, 25th IEEE Conference on Decision and Control, Athens, Greece, pp. 2037–2041.Search in Google Scholar

Sira-Ramírez, H. (1991). Non-linear discrete variable structure systems in quasi-sliding mode, International Journal of Control54(5): 1171–1187.10.1080/00207179108934203Search in Google Scholar

Soroush, M. and Kravaris, C. (1992). Discrete-time nonlinear controller synthesis by input/output linearization, AIChE Journal38(12): 1923–1945.10.1002/aic.690381209Search in Google Scholar

Spurgeon, S. and Davies, R. (1993). A nonlinear design approach for sliding mode control systems, Proceedings of the 32nd IEEE Conference on Decision and Control, San Antonio, TX, USA, Vol. 2, pp. 1440–1445.Search in Google Scholar

Spurgeon, S. and Pugh, A. (1991). On output deadbeat control of discrete-time multivariable systems, IEEE Transactions on Automatic Control36(7): 894–896.10.1109/9.85075Search in Google Scholar

Su, W.C., Drakunov, S.V. and Özgüner, Ü. (1994). Constructing discontinuity planes for variable structure systems—A Lyapunov approach, American Control Conference, Baltimore, MD, USA, Vol. 1, pp. 1169–1173.Search in Google Scholar

Su, W.-C., Drakunov, S.V. and Özgüner, Ü. (1996). Constructing discontinuity surfaces for variable structure systems: A Lyapunov approach, Automatica32(6): 925–928.10.1016/0005-1098(96)00017-9Search in Google Scholar

Tapia, A., Márquez, R., Bernal, M. and Cortez, J. (2014). Sliding subspace design based on linear matrix inequalities, Kybernetika50(3): 436–449.10.14736/kyb-2014-3-0436Search in Google Scholar

Utkin, V. (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., Guldner, J. and Shi, J. (1999). Sliding Mode Control in Electro-mechanical Systems, CRC Press, Boca Raton, FL.Search in Google Scholar

Utkin, V. and Yang, K. (1978). Methods for construction of discontinuity planes in multidimensional variable structure systems, Automation and Remote Control39(6): 1466–1470.Search in Google Scholar

Wang, Y., Xia, Z., Jiang, Z. and Xie, G. (2011). A quasi-sliding mode variable structure control algorithm for discrete-time and time-delay systems, Chinese Control and Decision Conference, Mianyang, China, pp. 107–110.Search in Google Scholar

Yadav, N. K. and Singh, R. (2012). Robust discrete-time nonlinear sliding mode controller with plant uncertainties, International Journal of Engineering, Science and Technology4(1): 38–45.10.4314/ijest.v4i1.5SSearch in Google Scholar

Yu, S., Yu, X. and Qian, W. (2000). Time delayed discrete variable structure control with quasi-sliding modes, in X. Yu and J.-X. Xu (Eds.), Advances in Variable Structure Systems: Analysis, Integration and Applications, World Scientific, Singapore, pp. 84–92.10.1142/9789812792082_0007Search in Google Scholar

Zhang, X., Wang, P., Yan, M. and Ju, Y. (2010). Discrete-time sliding mode control of nonlinear time-delay systems based on T–S fuzzy model, International Conference on Intelligent Control and Information Processing (ICICIP), Dalian, China, pp. 304–309.Search in Google Scholar