Skip to main content
SpringerLink
Log in

Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems

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

Abstract

This paper deals with the interval observer-based controller design for switched linear parameter-varying (LPV) systems with external disturbance and measurement noise. Firstly, with the help of positive system theory, we design asymptotic interval observers for the subsystems by giving the upper and the lower bounds of the disturbance and the measurement noise. Compared to the traditional observers, interval observers can manage with uncertainties better and provide the upper and the lower bounds for the state variables at any instant. Then, based on the new variable replacement method and multiple Lyapunov function method, we design an interval observer-based controller for the switched LPV systems and some sufficient conditions are obtained to guarantee the exponential stability of the closed-loop systems. Next, the corresponding solvability criteria for the interval observer-based controller are formulated. Finally, we provide a numerical example to illustrate the validity of the proposed results.

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

Similar content being viewed by others

Data Availability

The authors declare that the data supporting the findings of this study are available within the article.

References

  1. T. Binazadeh, M.S. Asadinia, A delay-dependent approach to finite-time \({H}_{\infty }\) control of nonlinear descriptor systems with state delay via observer-based control. Circ. Syst. Signal Process. 39(11), 5454–5474 (2020)

    Article  Google Scholar 

  2. S. Chebotarev, D. Efimov, T. Raissi, A. Zolghadri, On interval observer design for a class of continuous-time LPV systems. IFAC Proc. 46(23), 68–73 (2013)

    Article  Google Scholar 

  3. D. Efimov, L. Fridman, T. Raissi, A. Zolghadri, R. Seydou, Interval estimation for LPV systems applying high order sliding mode techniques. Automatica 48(9), 2365–2371 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Efimov, T. Raissi, S. Chebotarev, A. Zolghadri, Interval state observer for nonlinear time varying systems. Automatica 49(1), 200–205 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Efimov, T. Raissi, A. Zolghadri, Control of nonlinear and LPV systems: interval observer-based framework. IEEE Trans. Autom. Control 58(3), 773–778 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. H. Ethabet, D. Rabehi, D. Efimov, T. Raissi, Interval estimation for continuous-time switched linear systems. Automatica 90, 230–238 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  7. C.C. Fan, J. Lam, X.C. Xie, X.Q. Song, Observer-based output reachable set synthesis for periodic piecewise time-varying systems. Inf. Sci. 571, 246–261 (2021)

    Article  MathSciNet  Google Scholar 

  8. Z.Y. Fei, S. Shi, C. Zhao, L.G. Wu, Asynchronous control for 2-D switched systems with mode-dependent average dwell time. Automatica 79, 198–206 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  9. J.L. Gouze, A. Rapaport, M.Z. Hadj-Sadok, Interval observers for uncertain biological systems. Ecol. Model. 133(1), 45–56 (2000)

    Article  Google Scholar 

  10. Z.W. He, W. Xie, Control of non-linear switched systems with average dwell time: interval observer-based framework. IET Control Theory Appl. 10(1), 10–16 (2016)

    Article  MathSciNet  Google Scholar 

  11. J. Huang, X. Ma, H.C. Che, Z.Z. Han, Further result on interval observer design for discrete-time switched systems and application to circuit systems. IEEE Trans. Circuits Syst. II Exp. Briefs2 67(11), 2542–2546 (2020)

    Google Scholar 

  12. S. Ifqir, N. Ait-Oufroukh, D. Ichalal, S. Mammar, Synchronous interval observer design for switched LPV systems using multiple quadratic ISS-Lyapunov functions, in 2017 25th Mediterranean Conference on Control and Automation (MED), pp 388–393 (2017)

  13. J.T. Li, Z.H. Wang, W.H. Zhang, T. Raissi, Y. Shen, Interval observer design for continuous-time linear parameter-varying systems. Syst. Control Lett. 134, 104541 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  14. X.L. Li, X.Z. Lin, Y. Zou, Output feedback stabilization for planar switched nonlinear systems with asymmetric output constraints. Nonlinear Anal. Hybrid Syst. 40, 101005 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  15. D. Liberzon, Switching in systems and control (Birkhauser, Boston, MA, 2003)

    Book  MATH  Google Scholar 

  16. X.W. Liu, Q.C. Zhao, S.M. Zhong, Stability analysis of a class of switched nonlinear systems with delays: a trajectory-based comparison method. Automatica 91, 36–42 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  17. R.C. Ma, H.R. Zhang, S.Z. Zhao, Exponential stabilization of switched linear systems subject to actuator saturation with stabilizable and unstabilizable subsystems. J. Frankl. Inst. 358(1), 268–295 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  18. J. Mao, Z.R. Xiang, G.S. Zhai, Sampled-data control of a class of switched nonlinear systems under asynchronous switching. J. Frankl. Inst. 356(4), 1924–1943 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  19. N.H.A. Nguyen, S.H. Kim, Asynchronous \(H_{\infty }\) observer-based control synthesis of nonhomogeneous Markovian jump systems with generalized incomplete transition rates. Appl. Math. Comput. 411(3), 126532 (2021)

    MATH  Google Scholar 

  20. L. Nie, B. Cai, Y.M. Zhu, J.N. Yang, L.X. Zhang, Switched linear parameter-varying tracking control for quadrotors with large attitude angles and time-varying inertia. Optim. Control Appl. Methods 42(5), 1320–1336 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Oliveira, R. Renan Lima Pereira, On unknown input observers designs for discrete-time LPV systems with bounded rates of parameter variation. Eur. J. Control 58, 183–195 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  22. R.L. Pereira, M.S.D. Oliveira, Discrete-time LPV systems with inexact scheduling parameters: an unknown input observer design approach. Int. J. Gen. Syst. 51(1), 54–70 (2022)

    Article  MathSciNet  Google Scholar 

  23. D. Rabehi, D. Efimov, J.P. Richard, Interval estimation for linear switched system. IFAC-PapersOnLine 50(1), 6265–6270 (2017)

    Article  Google Scholar 

  24. H.L. Ren, G.D. Zong, D. Yang, Input-output finite-time stabilization for MJSs with time-varying delay: an observer-based approach. J. Frankl. Inst. 356(16), 9689–9712 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  25. Y. Shan, F.L. Zhu, Interval observer-based fault tolerant control strategy with fault estimation and compensation. Asian J. control 24(2), 895–906 (2022)

    Article  MathSciNet  Google Scholar 

  26. X.M. Sun, X.F. Wang, Y. Tan, X.L. Wang, W. Wang, Absolutely exponential stability and temperature control for gas chromatograph system under dwell time switching techniques. IEEE Trans. Cybern. 46(6), 1301–1310 (2016)

    Article  Google Scholar 

  27. X.L. Wang, H.S. Su, G.P. Jiang, Interval observer-based robust coordination control of multi-agent systems over directed networks. IEEE Trans. Circuits Syst. I Reg. Papers1 68(12), 5145–5155 (2021)

    Article  Google Scholar 

  28. Y.E. Wang, H.R. Karimi, D. Wu, Construction of hybrid interval observers for switched linear systems. Inf. Sci. 454, 242–254 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  29. Y.E. Wang, X.M. Sun, F. Mazenc, Stability of switched nonlinear systems with delay and disturbance. Automatica 69, 78–86 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  30. Z.C. Wang, G.L. Chen, H.Z. Ba, Stability analysis of nonlinear switched systems with sampled-data controllers. Appl. Math. Comput. 357, 297–309 (2019)

    MathSciNet  MATH  Google Scholar 

  31. Y. Xu, J.G. Dong, R.Q. Lu, L.H. Xie, Stability of continuous-time positive switched linear systems: a weak common copositive Lyapunov functions approach. Automatica 97, 278–285 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  32. D. Yang, J. Zhao, Feedback passification for switched LPV systems via a state and parameter-triggered switching with dwell time constraints. Nonlinear Anal. Hybrid Syst. 29, 147–164 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  33. C. Zammali, J.V. Gorp, T. Raissi, Interval estimation for continuous-time LPV switched systems. Int. J. Control 93(11), 2622–2633 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  34. J. Zhang, Y.G. Sun, Practical exponential stability of discrete-time switched linear positive systems with impulse and all modes unstable. Appl. Math. Comput. 409, 126408 (2021)

    MathSciNet  MATH  Google Scholar 

  35. J. Zhao, D.J. Hill, On stability, \(L_{2}\)-gain and \(H_{\infty }\) control for switched systems. Automatica 44(5), 1220–1232 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  36. J. Zhao, D.J. Hill, T. Liu, Synchronization of complex dynamical networks with switching topology: a switched system point of view. Automatica 45(11), 2502–2511 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. X.D. Zhao, H. Liu, J.F. Zhang, H.Y. Li, Multiple-mode observer design for a class of switched linear systems. IEEE Trans. Autom. Sci. Eng. 12(1), 272–280 (2015)

    Article  Google Scholar 

  38. Y. Zhao, D. Ma, J. Zhao, \(L_{2}\) bumpless transfer control for switched linear systems with almost output regulation. Syst. Control Lett. 119, 39–45 (2018)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China under Grants 62273218 and the National Key R &D Program of China under Grant 2018YFB1700100.

Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, China

    Jiaxiao Lv & Yue-E Wang

  2. Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology, Dalian, 116000, China

    Di Wu

Authors
  1. Jiaxiao Lv
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue-E Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Di Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yue-E Wang.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lv, J., Wang, YE. & Wu, D. Observer-Based Control for Continuous-Time Switched Linear Parameter-Varying Systems. Circuits Syst Signal Process 42, 2049–2064 (2023). https://doi.org/10.1007/s00034-022-02200-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-022-02200-6

Keywords

Search

Navigation