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An adaptive sliding mode control of delta operator systems with input nonlinearity containing unknown slope parameters

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Abstract

The problem of observer-based adaptive sliding mode control of delta operator systems with time-varying delays subject to input nonlinearity is investigated. The slope parameters of this nonlinearity are unmeasured. A novel adaptive control law is established such that the sliding surface in the state-estimation space can be reached in a finite time. A delay-dependent sufficient condition for the asymptotic stability of both the error system and the sliding mode dynamics is derived via linear matrix inequality (LMI). Finally, a simulation example is presented to show the validity and advantage of the proposed method.

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References

  1. Goodwin G C and Middleton R H, Rapprochement between continuous and discrete model reference adaptive control, Automatica, 1986, 22: 199–207.

    Article  MATH  Google Scholar 

  2. Ebert W, Optimal filtered predictive control—A delta operator approach, Syst. Control Lett., 2001 42: 69–80.

    Article  MathSciNet  MATH  Google Scholar 

  3. Fan H, Singular root distribution problem for delta-operator based real polynomials, Automatica, 1999, 35: 791–807.

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen S, Istepanian R H, Wu J, et al., Comparative study on optimizing closed-loop stability bounds of finite-precision controller structures with shift and delta operators, Syst. Control Lett., 2000, 40: 153–163.

    Article  MathSciNet  MATH  Google Scholar 

  5. Suchomski P, A J-lossless coprime factorisation approach to H ∞ control in delta domain, Automatica, 2002, 38: 1807–1814.

    Article  MathSciNet  MATH  Google Scholar 

  6. Guo X and Yang G, Non-fragile H8 filter design for delta operator formulated systems with circular region pole constraints: An LMI optimization approach, Acta Automat. Sinica, 2009, 35: 1209–1215.

    MathSciNet  MATH  Google Scholar 

  7. Soh C B, Robust stability of discrete-time systems using delta operator, IEEE T. Automat. Contr., 1991 35: 377–380.

    Article  MathSciNet  MATH  Google Scholar 

  8. Qiu J, Xia Y, Yang H, et al., Robust stabilisation for a class of discrete-time systems with time-varying delays via delta operators, IET Control Theory A, 2008, 2: 87–93.

    Article  MathSciNet  Google Scholar 

  9. Liu L, Han Z, and Li W, Global sliding mode control and application in chaotic systems, Nonlinear Dynam., 2009, 2: 193–198.

    Article  MathSciNet  MATH  Google Scholar 

  10. Wu L, Wang C, and Zeng Q, Observer-based sliding mode control for a class of uncertain nonlinear neutral delay systems, J. Franklin I., 2008, 345: 233–253.

    Article  MathSciNet  MATH  Google Scholar 

  11. Yang H, Xia Y, Fu M, et al., Robust adaptive sliding mode control for uncertain delta operator systems, Int. J. Adapt. Control, 2010, 24: 623–632.

    MathSciNet  MATH  Google Scholar 

  12. Xia Y, Fu M, Yang H, et al., Robust sliding mode control for uncertain time-delay systems based on delta operator, IEEE T. Ind. Electron., 2009, 56: 3646–3655.

    Article  Google Scholar 

  13. Yang H, Xia Y, and Shi P, Observer-based sliding mode control for a class of discrete systems via delta operator approach, J. Franklin I., 2010, 347: 1199–1213.

    Article  MathSciNet  MATH  Google Scholar 

  14. Gutierrez H M and Ro P I, Sliding-mode control of a nonlinear-input system: Application to a magnetically levitated fast-tool servo, IEEE T. Ind. Electron., 1998, 45: 921–927.

    Article  Google Scholar 

  15. Lin J, Yan J, and Liao T, Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity, Chaos Soliton Fract., 2005, 24: 371–381.

    Article  MathSciNet  MATH  Google Scholar 

  16. Werta J R, Spacecraft Attitude Determination and Control. Dordrecht, Holland: D, Reidel Publishing Company, 1978.

    Book  Google Scholar 

  17. Yu F, Chung H, and Chen S, Fuzzy sliding mode controller design for uncertain time-delayed systems with nonlinear input, Fuzzy Set Syst., 2003, 140: 359–374.

    Article  MathSciNet  MATH  Google Scholar 

  18. Xia Y, Chen J, Liu G P, et al., Robust adaptive sliding mode control for uncertain time-delay systems, Int. J. Adapt. Control Signal Process., 2009, 23: 863–881.

    Article  MathSciNet  MATH  Google Scholar 

  19. Cheng C C and Chien S H, Adaptive sliding mode controller design based on T-S fuzzy system models, Automatica, 2006, 42: 1005–1010.

    Article  MathSciNet  MATH  Google Scholar 

  20. Hung M L and Yan J J, Decentralized model-reference adaptive control for a class of uncertain large-scale time-varying delayed systems with series nonlinearities, Chaos, Solitons and Fractals, 2007, 33: 1558–1568.

    Article  MathSciNet  MATH  Google Scholar 

  21. Hu Q, Ma G, and Xie L, Robust and adaptive variable structure output feedback control of uncertain systems with input nonlinearity, Automatica, 2008, 44: 552–559.

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu L, Pu J, Song X, et al., Adaptive sliding mode control of uncertain chaotic systems with input nonlinearity, Nonlinear Dynamics, 2014, 76: 1857–1865.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. College of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, China

    Leipo Liu, Zhumu Fu & Xiaona Song

Authors
  1. Leipo Liu
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  2. Zhumu Fu
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  3. Xiaona Song
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Corresponding author

Correspondence to Leipo Liu.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. U1404610, 61473115, 61374077 and 61203047, Fundamental Research Project under Grant Nos. 142300410293, 142102210564 in the Science and Technology Department of Henan province, the Science and Technology Research Key Project under Grant No. 14A413001 in the Education Department of Henan Province.

This paper was recommended for publication by Editor LIU Yungang.

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Liu, L., Fu, Z. & Song, X. An adaptive sliding mode control of delta operator systems with input nonlinearity containing unknown slope parameters. J Syst Sci Complex 30, 535–549 (2017). https://doi.org/10.1007/s11424-016-5181-6

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  • DOI: https://doi.org/10.1007/s11424-016-5181-6

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