Skip to main content
SpringerLink
Log in

Finite-Time \(H_\infty \) Model Reference Control for Linear Systems Based on Average Dwell-Time Approach

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

This paper investigates the problem of state tracking for model reference control in a linear system with average dwell-time approach in a finite-time interval. Both matched and unmatched cases are taken into consideration in the system. The switching law is designed by the state error such that the considered tracking error is finite-time bounded and the considered system achieves a weighted \(H_\infty \) performance for the exogenous disturbance. With the aid of an error Lyapunov-like function and Schur complement lemma, the design of the switching law is formulated by linear matrix inequalities with sufficient conditions. A variable average dwell time is obtained that it is less than the traditional average dwell time in a finite-time interval. Finally, a numerical example is given to illustrate the effective design method of the switching law.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. R.P. Aguilera, A. Pablo, P. Lezana, G. Konstantinou, B. Wu, S. Bernet, V.G. Agelidis, Selective harmonic elimination model predictive control for multilevel power converters. IEEE Trans. Power Electron. 32(3), 2416–2426 (2017)

    Article  Google Scholar 

  2. A.A. Ahmed, B.K. Koh, H.S. Park, K.B. Lee, Y.I. Lee, Finite-control set model predictive control method for torque control of induction motors using a state tracking cost index. IEEE Trans. Ind. Electron. 64(3), 1916–1928 (2017)

    Article  Google Scholar 

  3. V.D. Blondel, A. Megretski, Unsolved problems in mathematical systems and control theory. IEEE Trans. Autom. Control 50(5), 746–746 (2005)

    Article  Google Scholar 

  4. H.H. Chiang, L.W. Lee, Optimized virtual model reference control for ride and handling performance-oriented semiactive suspension systems. IEEE Trans. Vehic. Technol. 64(5), 1679–1690 (2015)

    Article  Google Scholar 

  5. J. Fu, R.C. Ma, T.Y. Chai, Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica 54, 360–373 (2015)

    Article  MathSciNet  Google Scholar 

  6. H. Gao, B. Wu, D.W. Xu, M. Pande, R.P. Aguilera, Common-mode-voltage-reduced model-predictive control scheme for current-source-converter-fed induction motor drives. IEEE Trans. Power Electron. 32(6), 4891–4904 (2017)

    Article  Google Scholar 

  7. P.K. Gillella, X.Y. Song, Z.X. Sun, Time-varying internal model-based control of a camless engine valve actuation system. IEEE Trans. Control Syst. Technol. 22(4), 1498–1510 (2014)

    Article  Google Scholar 

  8. H. Habibullah, H.R. Pota, I.R. Petersen, M.S. Rana, Tracking of triangular reference signals using LQG controllers for lateral positioning of an AFM scanner stage. IEEE/ASME Trans. Mechatron. 19(4), 1105–1114 (2014)

    Article  Google Scholar 

  9. J.P. Hespanha, A.S. Morse, Stability of switched systems with average dwell time, in Proceedings of the 38th IEEE Conference on Decision and Control, Arizona, USA, pp. 2655–2660 (1999)

  10. J.S. Huang, C.Y. Wen, W. Wang, Y.D. Song, Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications. Automatica 69, 395–404 (2016)

    Article  MathSciNet  Google Scholar 

  11. H.K. Lam, H.Y. Li, Output-feedback tracking control for polynomial fuzzy-model-based control systems. IEEE Trans. Ind. Electron. 60(12), 5830–5840 (2013)

    Article  Google Scholar 

  12. X.Z. Lin, H.B. Du, S.H. Li, Finite-time boundedness and \(L_2\) gain analysis for switched delay systems with norm-bounded disturbance. Appl. Math. Comput. 217(12), 5982–5993 (2011)

    MathSciNet  MATH  Google Scholar 

  13. X.Z. Lin, H.B. Du, S.H. Li, Y. Zou, Finite-time boundedness and finite-time \(L_2\) gain analysis of discrete-time switched linear systems with average dwell time. J. Frankl. Inst. 350(4), 911–928 (2013)

    Article  Google Scholar 

  14. X.Z. Lin, H.B. Du, S.H. Li, Y. Zou, Finite-time stability and finite-time weighted L2-gain analysis for switched systems with time-varying delay. IET Control Theory Appl. 7(7), 1058–1069 (2013)

    Article  MathSciNet  Google Scholar 

  15. X.Z. Lin, C.X. Lv, S.H. Li, Y. Zou, Finite-time stability and finite-time boundedness for switched systems with sector bounded nonlinearities, in Proceedings of the 34th Chinese Control Conference, Hangzhou, China, pp. 651–656(2015)

  16. H. Liu, Y. Shen, X.D. Zhao, Asynchronous finite-time \(H_\infty \) control for switched linear systems via mode-dependent dynamic state-feedback. Nonlinear Anal. Hybrid Syst. 8, 109–120 (2013)

    Article  MathSciNet  Google Scholar 

  17. Y.F. Liu, J.Y. Yang, C.Z. Li, Robust finite-time stability and stabilisation for switched linear parameter-varying systems and its application to bank-to-turn missiles. IET Control Theory Appl. 9(14), 2171–2179 (2015)

    Article  MathSciNet  Google Scholar 

  18. A. Marian, F. Milano, A. Papachristodoulou, Algorithmic construction of Lyapunov functions for power system stability analysis. IEEE Trans. Circuits Syst. I Regul. Pap. 60(9), 2533–2546 (2013)

    Article  MathSciNet  Google Scholar 

  19. G. Mehdi, S. Mobayen, F. Tchier, Adaptive finite-time tracking control of uncertain non-linear n-order systems with unmatched uncertainties. IET Control Theory Appl. 10(14), 1675–1683 (2016)

    Article  MathSciNet  Google Scholar 

  20. B. Niu, J. Zhao, Robust stabilization and tracking control for a class of switched nonlinear systems. Asian J. Control 15(5), 1496–1502 (2013)

    MathSciNet  MATH  Google Scholar 

  21. H.C. Pangborn, A.G. Alleyne, Switched linear control for refrigerant superheat recovery in vapor compression systems. Control Eng. Pract. 57, 142–156 (2016)

    Article  Google Scholar 

  22. Z.H. Pang, G.P. Liu, D.H. Zhou, M.Y. Chen, Output tracking control for networked systems: a model-based prediction approach. IEEE Trans. Ind. Electron. 61(9), 4867–4877 (2014)

    Article  Google Scholar 

  23. B. Stellato, T. Geyer, P.J. Goulart, High-speed finite control set model predictive control for power electronics. IEEE Trans. Power Electron. 32(5), 4007–4020 (2017)

    Article  Google Scholar 

  24. L.V. Thanh, K. Turitsyn, Lyapunov function family approach to transient stability assessment. IEEE Trans. Power Syst. 31(2), 1269–1277 (2016)

    Article  Google Scholar 

  25. C.S. Tseng, B.S. Chen, \(L_\infty \)-gain fuzzy control for nonlinear dynamic systems with persistent bounded disturbances, in IEEE International Conference on Fuzzy Systems, pp. 783–788 (2004)

  26. M. Uddin, S. Mekhilef, M. Rivera, Experimental validation of minimum cost function-based model predictive converter control with efficient reference tracking. IET Power Electron. 8(2), 278–287 (2015)

    Article  Google Scholar 

  27. C.Y. Wu, J. Zhao, \(H_\infty \) adaptive tracking control for switched systems based on an average dwell-time method. Int. J. Syst. Sci. 46(14), 2547–2559 (2015)

    Article  MathSciNet  Google Scholar 

  28. L.G. Wu, J. Lam, Weighted \(H_\infty \) filtering of switched systems with time-varying delay: average dwell time approach. Circuits Syst. Signal Process. 28(6), 1017–1036 (2009)

    Article  MathSciNet  Google Scholar 

  29. L.G. Wu, X.B. Yang, F.B. Li, Nonfragile output tracking control of hypersonic air-breathing vehicles with an LPV model. IEEE/ASME Trans. Mechatron. 18(4), 1280–1288 (2013)

    Article  Google Scholar 

  30. W.M. Xiang, J. Xiao, Discussion on ”Stability, \(L_2\)-gain and asynchronous \(H_\infty \) control of discrete-time switched systems with average dwell time”. IEEE Trans. Autom. Control 57(12), 3259–3261 (2012)

    Article  Google Scholar 

  31. J. Xie, J. Zhao, Model reference adaptive control for switched LPV systems and its application. IET Control Theory Appl. 10(17), 2204–2212 (2016)

    Article  MathSciNet  Google Scholar 

  32. F.W. Yang, Z.D. Wang, W.C. Ho Daniel, M. Gani, Robust \(H_\infty \) control with missing measurements and time delays. IEEE Trans. Autom. Control 52(9), 1666–1672 (2007)

    Article  MathSciNet  Google Scholar 

  33. L.X. Zhang, H.J. Gao, Asynchronously switched control of switched linear systems with average dwell time. Automatica 46(5), 953–958 (2010)

    Article  MathSciNet  Google Scholar 

  34. S.Z. Zhao, M. Dimirovski, R.C.Ma. Georgi, Robust \(H_\infty \) control for non-minimum phase switched cascade systems with time delay. Asian J. Control 17(5), 1590–1599 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (61503071), Natural Science Foundation of Jilin Province (20180520211JH) and Science Research of Education Department of Jilin Province (201693, JJKH20170106KJ).

Author information

Authors and Affiliations

  1. School of Automation Engineering, Northeast Electric Power University, Jilin, 132012, Jilin, China

    Dongsheng Chen, Zhiqiang Wang & Qingyu Su

Authors
  1. Dongsheng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiqiang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Qingyu Su
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qingyu Su.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, D., Wang, Z. & Su, Q. Finite-Time \(H_\infty \) Model Reference Control for Linear Systems Based on Average Dwell-Time Approach. Circuits Syst Signal Process 37, 4773–4788 (2018). https://doi.org/10.1007/s00034-018-0801-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-018-0801-0

Keywords

Search

Navigation