This paper proposes a discrete-time sliding mode control (DT-SMC) algorithm for uncertain linear systems with time-varying delay on the state. The parameter uncertainties and the external disturbances are assumed to be unknown but norm-bounded. The sliding mode existence depends on that of the stable linear sliding surface, which is ensured by a sufficient condition that depends on the delay bounds and is derived using LMI. A numerical example as well as an application to the Two-Area Four-Machine power system has been presented to illustrate and confirm the usefulness and the effectiveness of the proposed control strategy.
BandyopadhyayBDeepakFPostlethwaiteIet al. (2010) A nonlinear sliding surface to improve performance of a discrete-time input-delay system. International Journal of Control83(9): 1895–1906.
2.
BartoszewiczA (1996) Remarks on discrete-time variable structure control systems. IEEE Transactions on Industrial Electronics43(1): 235–238.
3.
BoukhobzaTDjemaiMBarbotJP (1996) Nonlinear sliding observer for systems in output and output derivative injection form. In: Proceedings of 13th IFAC world congress, volume E, San Francisco, CA, 30 June–5 July, pp.299–305.
4.
BraytonR (1968) Small signal stability criterion for electrical networks containing lossless transmission lines. IBM Journal of Research and Development12(6): 431–440.
5.
Castillo-ToledoBDi GennaroSLoukianovAGet al. (2008) Discrete time sliding mode control with application to induction motors. Automatica44(12): 3036–3045.
6.
EdwardsCSpurgeonS (1996) Robust output tracking using a sliding mode controller: Observer scheme. International Journal of Control64(5): 967–983.
7.
FridmanE (2014) Introduction to Time-Delay Systems: Analysis and Control (Systems and Control: Foundations and Applications). Boston: Birkhäuser Basel.
8.
FuTJXietWF (2005) A novel sliding mode control of induction motor using space vector modulation technique. ISA Transactions44(4): 481–490.
9.
GaoHChenT (2007) New results on stability of discrete-time systems with time-varying state delay. IEEE transactions on Automatic Control52(2): 328–334.
10.
GaoWWangYHomaifaA (1995) Discrete-time variable structure control systems. IEEE Transactions on Industrial Electronics42(2): 117–122.
11.
GuKKharitonovVLChenJ (2003) Stability of Time-Delay Systems. Boston: Birkhäuser.
12.
HalanayARasvanV (1997) Stability radii for some propagation models. IMA Journal of Mathematical Control and Information14(1): 95–107.
13.
HuJWangZ (2013) Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties and randomly occurring nonlinearities. IEEE Transactions on Industrial Electronics59(7): 3008–3015.
14.
HuJWangZNiuYet al. (2014) Sliding mode control for uncertain discrete-time systems with Markovian jumping parameters and mixed delays. Journal of The Franklin Institute351(4): 2185–2202.
15.
IgnaciukPBartoszewiczA (2011) Discrete-time sliding-mode congestion control in multisource communication networks with time-varying delay. IEEE Transactions on Control Systems Technology19(4): 852–867.
16.
KumarRAgarwalSGoyalVet al. (2013) A discrete-time sliding mode controller for time-delay linear time-invariant systems with uncertainty. 5th International Conference on Computational Intelligence and Communication Networks, Mathura, India, 27–29 September, pp.233–236. Mathura, India: GLA University.
17.
KundurPBaluNLaubyM (1994) Power System Stability and Control. New York: McGraw-Hill.
18.
LiJChenZCaiDet al. (2015) Delay-dependent stability control for power system with multiple time delays. IEEE Transactions on Power Systems PP(99): 1–11.
19.
LinZXiaYShiPet al. (2011) Robust sliding mode control for uncertain linear discrete systems independent of time-delay. International Journal of Innovative Computing, Information and Control7(2): 869–880.
MusmadeBBPatreBM (2013) Feedforward-plus-sliding mode controller design with experimental application of coupled tank system. Transactions of the Institute of Measurement and Control35(8): 1058–1067.
22.
MusmadeBBPatreBM (2015) Sliding mode control design for robust regulation of time-delay processes. Transactions of the Institute of Measurement and Control37(6): 699–707.
23.
PaiMC (2008) Discrete-time output feedback sliding mode control for uncertain systems. Journal of Marine Science and Technology16(4): 295–300.
24.
PaiMC (2010) Discrete-time sliding mode control for uncertain systems with state and input delays. International Journal of Systems Science41(12): 1501–1510.
25.
PaiMC (2012) Robust discrete-time sliding mode control for multi-input uncertain time-delay system. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering226(7): 927–935.
26.
PaiMC (2013) Robust tracking and model following based on discrete-time neuro-sliding mode control for uncertain time-delay systems. Nonlinear Dynamics73(1–2): 427–437.
27.
SeungrohkOHassanKK (1995) Output feedback stabilization using variable structure control. International Journal of Control62(4): 831–848.
28.
SunNNiuYJiaT (2013) Sliding mode control for uncertain delay discrete-time systems with dead-zone saturation. Information and Control42, 478–483.
29.
UllahNHanSKhattakM (2015) Adaptive fuzzy fractional-order sliding mode controller for a class of dynamical systems with uncertainty. Transactions of the Institute of Measurement and Control.
30.
WuMHeYSheJHet al. (2004) Delay-dependent criteria for robust stability of time-varying delay systems. Automatica40(8): 1435–1439.
31.
XiaYFuMShiPet al. (2010) Robust sliding mode control for uncertain discrete-time systems with time delay. IET control theory and applications4(4): 613–624.
32.
XiaYLiuGPShiPet al. (2007) Sliding mode control of uncertain linear discrete time systems with input delay. IET Control Theory and Applications1(4): 1169–1175.
33.
XiaYZhuZLiCet al. (2010) Robust adaptive sliding mode control for uncertain discrete-time systems with time-delay. Journal of the Franklin Institute347(1): 339–357.
34.
YanMShiY (2008) Robust discrete-time sliding mode control for uncertain systems with time-varying state delay. IET Control Theory and Applications2(8): 662–674.
