Sliding mode control for time-varying delayed systems based on a reduced-order observer. (English) Zbl 1204.93029

Summary: A stabilisation problem for a class of nonlinear systems is considered, where both the nonlinear term and the nonlinear uncertainty are mismatched and subject to time-varying delay. Under the assumption that the delay is known, a reduced-order observer is designed using an appropriate transformation. A sliding surface is proposed in an augmented space formed by the system outputs and the estimated states. The sliding mode dynamics are derived using an equivalent control approach, and the Lyapunov-Razumikhin approach is exploited to analyse the stability of the sliding motion. Then, a sliding mode control law is developed such that the system can be driven to the sliding surface in finite time. A simulation example shows the effectiveness of the proposed approach.


93B12 Variable structure systems
93C10 Nonlinear systems in control theory
93D20 Asymptotic stability in control theory
93D30 Lyapunov and storage functions
Full Text: DOI


[1] Cheng, C.F., Output feedback stabilization for uncertain systems: constrained Riccati approach, IEEE transactions on automatic control, 43, 1, 81-84, (1998) · Zbl 0907.93049
[2] Choi, H.H., Output feedback variable structure control design with an \(H_2\) performance bound constraint, Automatica, 44, 9, 2403-2408, (2008) · Zbl 1153.93337
[3] Drakunov, S.V.; Perruquetti, W.; Richard, J.-P.; Belkoura, L., Delay identification in time-delay systems using variable structure observers, Annual reviews in control, 30, 2, 143-158, (2006)
[4] Edwards, C.; Spurgeon, S.K., Sliding mode control: theory and applications, (1998), Taylor and Francis Ltd. London
[5] Edwards, C.; Yan, X.G.; Spurgeon, S.K., On the solvability of the constrained Lyapunov problem, IEEE trans. on automat. control, 52, 10, 1982-1987, (2007) · Zbl 1366.93497
[6] Fridman, E.; Orlov, Y., Exponential stability of linear distributed parameter systems with time-varying delays, Automatica, 45, 1, 194-201, (2009) · Zbl 1154.93404
[7] Galimidi, A.R.; Barmish, B.R., The constrained Lyapunov problem and its application to robust output feedback stabilization, IEEE trans. on automat. control, 31, 5, 410-419, (1986) · Zbl 0591.93051
[8] Gu, K.; Kharitonov, V.L.; Chen, J., Stability of time-delay systems, (2003), Birkhäuser Boston · Zbl 1039.34067
[9] Janardhanan, S.; Bandyopadhyay, B., Output feedback discrete-time sliding mode control for time delay systems, IEE Proceedings part D: control theory and applications, 153, 4, 387-396, (2006) · Zbl 1132.93322
[10] Levaggi, L.; Punta, E., Analysis of a second-order sliding-mode algorithm in presence of input delays, IEEE trans. on automat. control, 51, 8, 1325-1332, (2006) · Zbl 1366.93101
[11] Lin, C.; Wang, Z.; Yang, F., Observer-based networked control for continuous-time systems with random sensor delays, Automatica, 45, 2, 578-584, (2009) · Zbl 1158.93349
[12] Luo, N.; De La Sen, M.; Rodellar, J., Robust stabilization of a class of uncertain time delay systems in sliding mode, International journal of robust and nonlinear control, 7, 1, 59-74, (1997) · Zbl 0878.93055
[13] Niu, Y.; Ho, D., Robust observer design for ito stochastic time-delay systems via sliding mode control, Systems & control letters, 55, 10, 781-793, (2006) · Zbl 1100.93047
[14] Niu, Y.; Lam, J.; Wang, X.; Ho, D., Observer-based sliding mode control for nonlinear state-delayed systems, International journal of systems science, 35, 2, 139-150, (2004) · Zbl 1059.93025
[15] Richard, J.P., Time-delay systems: an overview of some recent advances and open problems, Automatica, 39, 10, 1667-1694, (2003) · Zbl 1145.93302
[16] Saffer, D.R.; Castro, J.J.; Doyle, F.J., A variable time delay compensator for multivariable linear processes, Journal of process control, 15, 2, 215-222, (2005)
[17] Shtessel, Y.B.; Zinober, A.S.I.; Shkolnikov, I.A., Sliding mode control for nonlinear systems with output delay via method of stable system center, ASME journal dynamics systems, measurement and control, 125, 2, 253-257, (2003)
[18] Suplin, V.; Shaked, U., Robust \(H_\infty\) output-feedback control of systems with time-delay, Systems & control letters, 57, 3, 193-199, (2008) · Zbl 1129.93379
[19] Utkin, V.I., Sliding modes in control optimization, (1992), Springer-Verlag Berlin · Zbl 0748.93044
[20] Wang, Z.; Ho, D.; Liu, Y.; Liu, X., Robust \(H_\infty\) control for a class of nonlinear discrete time-delay stochastic systems with missing measurements, Automatica, 45, 3, 684-691, (2009) · Zbl 1166.93319
[21] Yan, X.G.; Spurgeon, S.K.; Edwards, C., Decentralised sliding mode control for nonminimum phase interconnected systems based on a reduced-order compensator, Automatica, 42, 10, 1821-1828, (2006) · Zbl 1114.93035
[22] Yan, X.G.; Wang, J.J.; Lü, X.Y.; Zhang, S.Y., Decentralized output feedback robust stabilization for a class of nonlinear interconnected systems with similarity, IEEE trans. on automat. control, 43, 2, 294-299, (1998) · Zbl 0906.93003
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