Robust discrete-time sliding mode control for uncertain systems with time-varying state delay
Robust discrete-time sliding mode control for uncertain systems with time-varying state delay
- Author(s): M. Yan and Y. Shi
- DOI: 10.1049/iet-cta:20070460
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): M. Yan 1, 2 and Y. Shi 2
-
-
View affiliations
-
Affiliations:
1: School of Electronics and Control Engineering, Chang'an University, Xi'an, People's Republic of China
2: Department of Mechanical Engineering, University of Saskatchewan, Saskatoon, Canada
-
Affiliations:
1: School of Electronics and Control Engineering, Chang'an University, Xi'an, People's Republic of China
- Source:
Volume 2, Issue 8,
August 2008,
p.
662 – 674
DOI: 10.1049/iet-cta:20070460 , Print ISSN 1751-8644, Online ISSN 1751-8652
A robust discrete-time sliding mode control (DT-SMC) for uncertain linear systems with unknown time-varying state delay is analysed, in which uncertainties consist of mismatched uncertain parameters and unknown bounded nonlinear function. By using the linear matrix inequality approach, a sufficient condition for the existence of stable sliding surfaces depending on the lower and upper delay bounds is established. On the basis of this existence condition, the synthesised DT-SMC can guarantee the sliding mode reaching condition of the specified discrete-time sliding surface. Two examples verify the effectiveness of the proposed method.
Inspec keywords: discrete time systems; time-varying systems; uncertain systems; robust control; delays; linear matrix inequalities; variable structure systems; linear systems
Other keywords:
Subjects: Discrete control systems; Stability in control theory; Time-varying control systems; Multivariable control systems; Algebra; Distributed parameter control systems
References
-
-
1)
- L. Zhang , Y. Shi , T. Chen , B. Huang . A new method for stabilization of networked control systems with random delays. IEEE Trans. Autom. Control , 8 , 1177 - 1181
-
2)
- M. Wu , Y. He , J. She , G. Liu . Delay-dependent criteria for robust stability of time-varying delay systems. Automatica , 8 , 1435 - 1439
-
3)
- Y. Niu , D.W.C. Ho , J. Lam . Robust integral sliding mode control for uncertain stochastic systems with time-varying delay. Automatica , 873 - 880
-
4)
- S. Janardhanan , B. Bandyopadhyay . Output feedback discrete-time sliding mode control for time delay systems. IEE Proc., Control Theory Appl. , 4 , 387 - 396
-
5)
- E.G. Laurent , O. Francois , A. Mustapha . A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
-
6)
- V. Utkin . Variable structure systems with sliding modes. IEEE Trans. Autom. Control , 2 , 212 - 222
-
7)
- K. Gu , V.L. Kharitonov , J. Chen . (2003) Stability of time-delay systems.
-
8)
- H. Gao , J. Lam , C. Wang , Y. Wang . Delay-dependent output-feedback stabilization of discrete-time systems with time-varying state delay. IEE Proc. Control Theory Appl. , 6 , 691 - 698
-
9)
- S. Janardhanan , B. Bandyopadhyay . Discrete sliding mode control of systems with unmatched uncertainty using multirate output feedback. IEEE Trans. Autom. Control , 6 , 1030 - 1035
-
10)
- S. Boyd , L.E. Ghaoui , E. Feron , V. Balakrishnan . (1994) Linear matrix inequalities in system and control theory.
-
11)
- Y.S. Moon , P.G. Park , W.H. Kwon , Y.S. Lee . Delay-dependent robust stabilization of uncertain state-delayed systems. Int. J. Control , 14 , 1447 - 1455
-
12)
- Zheng, Y., Dimirovski, G.M., Jing, Y., Yang, M.: `Discrete-time sliding mode control of nonlinear systems', Proc. 2007 American Control Conf., 2007, New York, USA, p. 3825–3830.
-
13)
- H. Gao , T. Chen . New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Control , 2 , 328 - 334
-
14)
- Y. Xia , G.-P. Liu , P. Shi , J. Chen , D. Rees . Robust delay-dependent sliding mode control for uncertain time-delay systems. Int. J. Robust Nonlinear Control , 11 , 1142 - 1161
-
15)
- L. Xie . Output feedback H∞ control of systems with parameter uncertainty. Int. J. Control , 4 , 741 - 750
-
16)
- K. Tanaka , H.O. Wang . (2001) Fuzzy control systems design and analysis.
-
17)
- Y. Niu , J. Lam , X. Wang . Sliding-mode control for uncertain neutral delay systems. Int. J. Syst. Sci. , 2 , 139 - 150
-
18)
- B. Xu , Y. Lin . An improved Razuminkhin-type theorem and its applications. IEEE Trans. Autom. Control , 4 , 839 - 841
-
19)
- P. Park , J.W. Ko . Stability and robust stability for systems with a time-varying delay. Automatica , 1855 - 1858
-
20)
- W. Gao , Y. Wang , A. Homaifa . Discrete-time variable structure control systems. IEEE Trans. Ind. Electron. , 117 - 122
-
21)
- Y.Q. Xia , Y.M. Jia . Robust sliding-mode control for uncertain time-delay systems: an LMI approach. IEEE Trans. Autom. Control , 6 , 1086 - 1092
-
22)
- A. Bartoszewicz . Remarks on ‘Discrete-time variable structure control systems. IEEE Trans. Ind. Electron. , 1 , 235 - 238
-
23)
- Koshkouei, A.J., Zinober, A.S.I.: `Sliding mode time delay systems', Proc. IEEE Workshop on variable structure control, 1996, Tokyo, Japan, p. 97–101.
-
24)
- M. Vidyasagar . (2002) Nonlinear systems analysis.
-
25)
- C.Y. Tang , E.A. Misawa . Discrete variable structure control for linear multivariable systems. J. Dyn. Syst., Meas. Control , 783 - 792
-
1)