Sliding-mode control of uncertain systems in the presence of unmatched disturbances with applications. (English) Zbl 1205.93060

Summary: This article considers the development of constructive sliding-mode control strategies based on measured output information only for linear, time-delay systems with bounded disturbances that are not necessarily matched. The novel feature of the method is that linear matrix inequalities are derived to compute solutions to both the existence problem and the finite time reachability problem that minimise the ultimate bound of the reduced-order sliding-mode dynamics in the presence of state time-varying delay and unmatched disturbances. The methodology provides guarantees on the level of closed-loop performance that will be achieved by uncertain systems which experience delay. The methodology is also shown to facilitate sliding-mode controller design for systems with polytopic uncertainties, where the uncertainty may appear in all blocks of the system matrices. A time-delay model with polytopic uncertainties from the literature provides a tutorial example of the proposed method. A case study involving the practical application of the design methodology in the area of autonomous vehicle control is also presented.


93C05 Linear systems in control theory
93B52 Feedback control
Full Text: DOI


[1] DOI: 10.1016/S0005-1098(98)80021-6 · Zbl 0937.93039
[2] DOI: 10.1016/S0005-1098(01)00211-4 · Zbl 0991.93021
[3] DOI: 10.1109/9.763227 · Zbl 0956.93028
[4] DOI: 10.1016/j.automatica.2004.05.004 · Zbl 1079.93014
[5] DOI: 10.1109/9.898702 · Zbl 1056.93638
[6] DOI: 10.1080/00207179508921587 · Zbl 0849.93012
[7] El-Khazali R, IEEE Transactions on Automatic Control 31 pp 805– (1995)
[8] Fernando C, IEEE Transactions on Automatic Control 51 pp 853– (2006) · Zbl 1366.93094
[9] Fridman E, Systems and Control Letters 42 pp 233– (2001) · Zbl 0985.93006
[10] Fridman E, Automatica 10 pp 2258– (2009) · Zbl 1179.93089
[11] DOI: 10.1080/00207170310001633286 · Zbl 1049.93012
[12] DOI: 10.1016/S0167-6911(01)00199-2 · Zbl 0994.93004
[13] DOI: 10.1109/TIE.2009.2023635
[14] DOI: 10.1016/j.automatica.2006.08.015 · Zbl 1111.93073
[15] DOI: 10.1109/TSMCB.2005.856145
[16] DOI: 10.1080/00207720500156363 · Zbl 1078.93013
[17] DOI: 10.1080/0020717031000147511 · Zbl 1036.93005
[18] DOI: 10.1109/TAC.2008.2010889 · Zbl 1367.93129
[19] DOI: 10.1109/TAC.2003.811270 · Zbl 1364.93287
[20] Yao L, SEAS DTC Technical Conference (2006)
[21] DOI: 10.1109/9.241564 · Zbl 0790.93027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.