Skip to main content
SpringerLink
Log in

Controller Design for Switched Systems with Non-symmetrical Input Saturation

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

Abstract

In this paper, a state feedback controller is designed for switched systems with non-symmetrical input saturation based on two classes of parametric Riccati equation (PRE). Through appropriate mathematical transformation, we transform a switched system with non-symmetrical input saturation to a switched system with multiple equilibrium points and symmetrical input saturation. The exponential stability of the switched system is investigated using the good properties of PRE. The main contributions of this paper include (a) solving the non-symmetrical input saturation control problem for the switched system; (b) designing a controller to guarantee the exponential stability of the switched system with the subsystems having the open-loop critical stable poles; (c) the designed controller can be easily computed by solving the PRE. The controller is easy to implement in practical applications. A numerical example is provided to illustrate the effectiveness and potential of the proposed method.

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
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  1. A. Benzaouia, M. Benhayoun, F. Mesquine, Stabilization of systems with unsymmetrical saturated control: an LMI approach. Circuits Syst. Signal Process. 33(10), 3263–3275 (2014)

    Article  MathSciNet  Google Scholar 

  2. D.Z. Cheng, Y.Q. Guo, Advances on switched systems. Control Theory Appl. 22(6), 954–960 (2005)

    Google Scholar 

  3. Y.G. Chen, S.M. Fei, K.J. Zhang et al., Control synthesis of discrete-time switched linear systems with input saturation based on minimum dwell time approach. Circuits Syst. Signal Process. 31(2), 779–795 (2012)

    Article  MathSciNet  Google Scholar 

  4. G.D. Chen, Y.Z. Sun, C.H. An et al., Measurement and analysis for frequency domain error of ultra-precision spindle in a flycutting machine tool. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 232(9), 1501–1507 (2018)

    Article  Google Scholar 

  5. Y.G. Chen, S.M. Fei, K.J. Zhang et al., Control of switched linear systems with actuator saturation and its applications. Math. Comput. Modell. 56(1–2), 14–26 (2012)

    Article  MathSciNet  Google Scholar 

  6. D.S. Du, B. Jiang, P. Shi et al., \(H_{\infty }\) filtering of discrete-time switched systems with state delays via switched Lyapunov function approach. IEEE Trans. Autom. Control 52(8), 1520–1525 (2007)

    Article  MathSciNet  Google Scholar 

  7. S.L. Dong, C.L.P. Chen, M. Fang et al., Dissipativity-based asynchronous fuzzy sliding mode control for T-S fuzzy hidden Markov jump systems. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2919299

    Article  Google Scholar 

  8. G.R. Duan, H.H. Yu, LMIs in Control Systems: Analysis, Design and Applications (CRC Press, Boca Raton, 2013)

    Book  Google Scholar 

  9. M. Fang, P. Shi, S.L. Dong, Sliding mode control for Markov jump systems with delays via asynchronous approach (Syst. Man Cybern. Syst, IEEE Trans, 2019). https://doi.org/10.1109/TSMC.2019.2917926

    Book  Google Scholar 

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

  11. H. Lin, P.J. Antsaklis, Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Trans. Autom. Control 54(2), 308–322 (2009)

    Article  MathSciNet  Google Scholar 

  12. D. Liberzon, A.S. Morse, Basic problems in stability and design of switched systems. IEEE Control Syst. Mag. 19(5), 59–70 (1999)

    Article  Google Scholar 

  13. Z.L. Lin, Low Gain Feedback (Springer, London, 1998)

    Google Scholar 

  14. X.D. Li, P. Li, Q.G. Wang, Input/output-to-state stability of impulsive switched systems. Syst. Control Lett. 116, 1–7 (2018)

    Article  MathSciNet  Google Scholar 

  15. W. Ni, D.Z. Cheng, Control of switched linear systems with input saturation. Int. J. Syst. Sci. 41(9), 1057–1065 (2010)

    Article  MathSciNet  Google Scholar 

  16. Y.B. Qian, Z.R. Xiang, H.R. Karimi, Disturbance tolerance and rejection of discrete switched systems with time-varying delay and saturating actuator. Nonlinear Anal. Hybrid Syst. 16(1), 81–92 (2015)

    Article  MathSciNet  Google Scholar 

  17. M.P. Ran, Q. Wang, C.Y. Dong, Stabilization of a class of nonlinear systems with actuator saturation via active disturbance rejection control. Automatica 63, 302–310 (2016)

    Article  MathSciNet  Google Scholar 

  18. Y. Shen, Z.G. Wu, P. Shi et al., Dissipativity based fault detection for 2D Markov jump systems with asynchronous modes. Automatica 106, 8–17 (2019)

    Article  MathSciNet  Google Scholar 

  19. Q. Wang, A.K. Xue, Reliable gain scheduling output tracking control for spacecraft rendezvous. Int. J. Control Autom. Syst. 16(1), 234–242 (2018)

    Article  Google Scholar 

  20. Y. Wu, T.S. Liu, Y.P. Wu et al., \(H_{\infty }\) output tracking control for uncertain networked control systems via a switched system approach. Int. J. Robust Nonlinear Control 26(5), 995–1009 (2016)

    Article  MathSciNet  Google Scholar 

  21. Q. Wang, K. Zhang, A.K. Xue et al., Reliable robust control for the system with input saturation based on gain scheduling. Circuits Syst. Signal Process. 36(6), 2586–2604 (2017)

    Article  MathSciNet  Google Scholar 

  22. Q. Wang, Z.G. Wu, P. Shi et al., Robust control for switched systems subject to input saturation and parametric uncertainties. J. Frankl. Inst. 354(16), 7266–7279 (2017)

    Article  MathSciNet  Google Scholar 

  23. Q. Wang, A.K. Xue, Robust control for spacecraft rendezvous system with actuator unsymmetrical saturation: a gain scheduling approach. Int. J. Control 91(6), 1241–1250 (2018)

    Article  MathSciNet  Google Scholar 

  24. S. Yin, H.J. Gao, J.B. Qiu et al., Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults. Automatica 76, 282–292 (2017)

    Article  MathSciNet  Google Scholar 

  25. W. Yang, S.C. Tong, Output feedback robust stabilization of switched fuzzy systems with time-delay and actuator saturation. Neurocomputing 164, 173–181 (2015)

    Article  Google Scholar 

  26. L. Zhang, P. Shi, \({l_{2}}\) -gain and asynchronous \({H_{{\infty }}}\) control of discrete-time switched systems with average dwell time. IEEE Trans. Autom. Control 54(9), 2192–2199 (2009)

    Article  MathSciNet  Google Scholar 

  27. B. Zhou, Analysis and design of discrete-time linear systems with nested actuator saturations. Syst. Control Lett. 62(10), 871–879 (2013)

    Article  MathSciNet  Google Scholar 

  28. B. Zhou, G.R. Duan, Z.Y. Li, On improving transient performance in global control of multiple integrators system by bounded feedback. Syst. Control Lett. 57(10), 867–875 (2008)

    Article  MathSciNet  Google Scholar 

  29. L.X. Zhang, N.G. Cui, M. Liu et al., Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Trans. Circuits Syst. I Regul. Pap. 58(5), 1109–1118 (2011)

    Article  MathSciNet  Google Scholar 

  30. X.Q. Zhao, J. Zhao, \(L_{2}-\) Gain analysis and output feedback control for switched delay systems with actuator saturation. J. Frankl. Inst. 352(7), 2646–2664 (2015)

    Article  Google Scholar 

  31. B. Zhou, G.R. Duan, Z.L. Lin, A parametric Lyapunov equation approach to the design of low gain feedback. IEEE Trans. Autom. Control 53(6), 1548–1554 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the Zhejiang Provincial Natural Science Foundation of China (LY18F030005, LR16F030003), the China Postdoctoral Science Foundation (2018M632464), the National Natural Science Foundations of China (61503105, 61973102).

Author information

Authors and Affiliations

  1. State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, 310027, China

    Qian Wang & Zhengguang Wu

  2. Institute of Information and Control, Hangzhou Dianzi University, Hangzhou, 310018, China

    Qian Wang & Yun Chen

Authors
  1. Qian Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengguang Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qian 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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Q., Wu, Z. & Chen, Y. Controller Design for Switched Systems with Non-symmetrical Input Saturation. Circuits Syst Signal Process 40, 136–153 (2021). https://doi.org/10.1007/s00034-020-01476-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01476-w

Keywords

Search

Navigation