Skip to main content
SpringerLink
Log in

Stabilization of a Class of Hybrid Systems by Switching Controllers with Input Constraints

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

Abstract

In this paper, a hybrid control strategy using appropriate switching between a set of linear controllers is presented for stabilization of a class of hybrid systems with input constraints. The input constraints under consideration are novel reverse polytopic constraints avoiding a set of specified input values. The design procedure of the switching controllers is performed by solving a set of linear matrix inequalities for the full state feedback case and by solving a set of bilinear matrix inequalities for the output feedback case. Under the designed controllers, the closed-loop system is shown to be globally uniformly pre-asymptotically stable if a specific set of matrix inequalities ensuring the existence of a common Lyapunov function are satisfied. To avoid the Zeno behavior, a tunable parameter related to the controller gains is introduced and assessed. It is shown that the proposed switching control is superior to continuous state feedback control with input constraints. In addition, besides continuous linear systems, the proposed control strategy is applicable to hybrid or impulsive systems. Numerical examples are included to illustrate 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

References

  1. L. Berardi, E. De Santis, M.D. Di Benedetto, Control of switching systems under state and input constraints, in The 1999 European Control Conference (1999), pp. 1778–1783

  2. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

    Book  Google Scholar 

  3. A. Brondsted, An Introduction to Convex Polytopes (Springer, New York, 2012)

    MATH  Google Scholar 

  4. C. Cai, S. Mijanovic, LMI-based stability analysis of linear hybrid systems with application to switched control of a refrigeration process. Asian J. Control 14(1), 12–22 (2012)

    Article  MathSciNet  Google Scholar 

  5. P. Casau, R.G. Sanfelice, C. Silvestre, Hybrid stabilization of linear systems with reverse polytopic input constraints. IEEE Trans. Autom. Control 62(12), 6473–6480 (2017)

    Article  MathSciNet  Google Scholar 

  6. P. Casau, R.G. Sanfelice, R. Cunha, D. Cabecinhas, C. Silvestre, A hybrid feedback controller for robust global trajectory tracking of quadrotor-like vehicles with minimized attitude error, in Proceedings of the IEEE International Conference on Robotics and Automation (2014), pp. 6272–6277

  7. G. Chen, J. Li, Y. Yang, Finite time stability and stabilization of hybrid dynamic systems. J. Syst. Eng. Electron. 21(6), 1084–1089 (2010)

    Article  Google Scholar 

  8. R. Goebel, R.G. Sanfelice, A.R. Teel, Hybrid dynamical systems. IEEE Control Syst. Mag. 29(2), 28–93 (2009)

    Article  MathSciNet  Google Scholar 

  9. K.A. Hamed, R.D. Gregg, Decentralized feedback controllers for robust stabilization of periodic orbits of hybrid systems: application to bipedal walking. IEEE Trans. Control Syst. Technol. 25(4), 1153–1167 (2017)

    Article  Google Scholar 

  10. M.D. Hua, T. Hamel, P. Morin, C. Samson, A control approach for thrust-propelled underactuated vehicles and its application to VTOL drones. IEEE Trans. Autom. Control 54(8), 1837–1853 (2009)

    Article  MathSciNet  Google Scholar 

  11. S. Kanev, C. Scherer, M. Verhaegen, B. De Schutter, Robust output-feedback controller design via local BMI optimization. Automatica 40(7), 1115–1127 (2004)

    Article  MathSciNet  Google Scholar 

  12. N. Kapoor, P. Daoutidis, Stabilization of systems with input constraints. Int. J. Control 66(5), 653–676 (1997)

    Article  MathSciNet  Google Scholar 

  13. X. Li, Global exponential stability of impulsive delay systems with flexible impulse frequency. IEEE Trans. Syst. Man Cybern. Syst. 99, 1–9 (2017)

    Google Scholar 

  14. Y. Li, Impulsive synchronization of stochastic neural networks via controlling partial states. Neural Process. Lett. 46(1), 59–69 (2017)

    Article  Google Scholar 

  15. X. Li, J. Cao, An impulsive delay inequality involving unbounded time-varying delay and applications. IEEE Trans. Autom. Control 62(7), 3618–3625 (2017)

    Article  MathSciNet  Google Scholar 

  16. Y. Li, B. Li, Y. Liu, J. Lu, Set stability and stabilization of switched Boolean networks with state-based switching. IEEE Access 6, 35624–35630 (2018)

    Article  Google Scholar 

  17. H. Li, Y. Wang, Controllability analysis and control design for switched Boolean networks with state and input constraints. SIAM J. Control Optim. 53(5), 2955–2979 (2015)

    Article  MathSciNet  Google Scholar 

  18. D. Liberzon, Switching in Systems and Control (Springer, New York, 2003)

    Book  Google Scholar 

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

    Article  Google Scholar 

  20. Z. Liu, R. Pei, X. Mu, J. Zhang, State feedback controller design for a class of hybrid systems with time-delay under input constraints, in Proceedings of the 1st International Symposium on Systems and Control in Aerospace and Astronautics (2006), pp. 877–880

  21. X. Lou, Y. Li, R.G. Sanfelice, Robust stability of hybrid limit cycles with multiple jumps in hybrid dynamical systems. IEEE Trans. Autom. Control 63(4), 1220–1226 (2018)

    Article  MathSciNet  Google Scholar 

  22. X. Lou, J.A.K. Suykens, Hybrid coupled local minimizers. IEEE Trans. Circuits Syst. I Regul. Pap. 61(2), 542–551 (2014)

    Article  Google Scholar 

  23. C. Prieur, A.R. Teel, L. Zaccarian, Relaxed persistent flow/jump conditions for uniform global asymptotic stability. IEEE Trans. Autom. Control 59(10), 2766–2771 (2014)

    Article  MathSciNet  Google Scholar 

  24. R.G. Sanfelice, R. Goebel, A.R. Teel, Invariance principles for hybrid systems with connections to detectability and asymptotic stability. IEEE Trans. Autom. Control 52(12), 2282–2297 (2007)

    Article  MathSciNet  Google Scholar 

  25. A. Singh, J.P. Hespanha, Stochastic hybrid systems for studying biochemical processes. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 368, 4995–5011 (2010)

    Article  MathSciNet  Google Scholar 

  26. H. Sussmann, E. Sontag, Y. Yang, A general result on the stabilization of linear systems using bounded controls, in Proceedings of the 32nd IEEE Conference on Decision and Control (1993), pp. 1802–1807

  27. X. Yang, J. Lu, Finite-time synchronization of coupled networks with Markovian topology and impulsive effects. IEEE Trans. Autom. Control 61(8), 2256–2261 (2016)

    Article  MathSciNet  Google Scholar 

  28. X. Yang, J. Lu, D.W.C. Ho, Q. Song, Synchronization of uncertain hybrid switching and impulsive complex networks. Appl. Math. Model. 59, 379–392 (2018)

    Article  MathSciNet  Google Scholar 

  29. Q. Ye, X. Lou, Impulsive control for target estimation in sensor networks. Circuits Syst. Signal Process. 38(1), 442–454 (2019)

    Article  MathSciNet  Google Scholar 

  30. X. Zhu, Y. Xia, M. Wang, S. Ma, \(H_\infty \) fault detection for discrete-time hybrid systems via a descriptor system method. Circuits Syst. Signal Process. 33(9), 2807–2826 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi, 214122, China

    Xin Zhang & Xuyang Lou

  2. School of Science, Jiangnan University, Wuxi, 214122, China

    Zhengxian Jiang

Authors
  1. Xin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xuyang Lou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhengxian Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xuyang Lou.

Additional information

Publisher's Note

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

This work is supported by National Natural Science Foundation of China (61807016) and Postdoctoral Science Foundation of China (2018M642160).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, X., Lou, X. & Jiang, Z. Stabilization of a Class of Hybrid Systems by Switching Controllers with Input Constraints. Circuits Syst Signal Process 39, 1649–1664 (2020). https://doi.org/10.1007/s00034-019-01213-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01213-y

Keywords

Search

Navigation