Skip to main content
SpringerLink
Log in

Static Output Feedback Stabilization of a Class of Switched Linear Systems with State Constraints

  • Regular Paper
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper will research the problem of static output feedback (SOF) stabilization of state-constrained switched linear systems via an improved average dwell time method (ADT). Firstly, an improved ADT method is adopted to establish sufficient conditions for SOF of the state-constrained switched linear systems in the form of matrix inequality. It has been shown that this method is less conservative than traditional ADT, which in view of different decay rates of a Lyapunov function related to an active subsystem on the basis of whether the saturations occur or not. Then, a new iterative algorithm is designed to solve the matrix inequality and a SOF controller can be added. In the iterative linear matrix inequality (ILMI) algorithm, it is important not only to overcome the typical bilinear matrix inequality (BMI) problem of SOF, but also to solve the non-convex problem caused by state constraints. Finally, the availability and the applicability of the proposed method is shown by the application of a boost converter.

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

Similar content being viewed by others

References

  1. Y. Y. Liu and G. S. Stojanovski, “Feedback passivation of switched nonlinear systems using storage-like fuctions,” International Journal of Control, vol. 9, no. 5, pp. 980–986, 2011. [click]

    Google Scholar 

  2. J. Fun, R. C. Ma, and T. Y. Chai, “Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers,” Automatical, vol. 54, pp. 360–373, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  3. L. H. Zhao and G. O. Shi, “A model following control syatem for nonlinear descriptor systems,” Journal of Northeast Dianli University, vol. 32, no. 4, pp. 87–90, 2012.

    Google Scholar 

  4. Y. M. Li, S. Sui, and S. C. Tong, “Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics,” IEEE Transactions on Cybernetics, vol. 47, no. 2, pp. 403–414, 2017. [click]

    Google Scholar 

  5. H. Richter, “A multi-regulator sliding mode control strategy for output-constrained system,” Automatica, vol. 47, no. 10, pp. 2251–2259, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. B. Niu and X. D. Zhao, “A new control method for stateconstrained nonlinear switched systems with application to chemical process,” International Journal of Control, vol. 88, no. 9, pp. 1693–1701, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. T. Iwasaki and R. E. Skelton, “Linear quadratic suboptimal control with static output feedback,” Syst. Control Lett., vol. 23, pp. 421–430, 1994. [click]

    Article  MathSciNet  MATH  Google Scholar 

  8. V. Kucera and C. E. de Souza, “A necessary and sufficient condition for output feedback stabilizability,” Automatica, vol. 31, no. 9, pp. 1357–1359, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. L. Syrmos, C. T. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback - a survey,” Automatica, vol. 33, no. 2, pp. 125–137, 1997. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. C. Duan and F. Wu, “Output-feedback control for switched linear systems subject to actuator saturation,” International Journal of Control, vol. 85, no. 10, pp. 1532–1545, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  11. X. D. Zhao, S. Yin, H. Y. Li, and B. Niu, “Switching stabilization for a class of slowly switched systems,” IEEE Transactions on Automatic Control, vol. 60, no. 1, pp. 221–226, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. X. D. Zhao, P. Shi, Y. F. Yin, and S. K. Nguang, “New results on stability of slowly switched systems: a multiple discontinuous Lyapunov function approach,” IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3502–3509, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  13. X. D. Zhao, Y. F. Yin, B. Niu, and X. L. Zheng, “Stabilization for a class of switched nonlinear systems with novel average dwell time switching by T-S fuzzy modeling,” IEEE Transactions on Cybernetics, vol. 46, no. 8, pp. 1952–1957, 2015.

    Article  Google Scholar 

  14. R. Guo and Y. Wang, “Stability analysis for a class of switched linear systems,” Asian Journal of Control, vol. 14, no. 3, pp. 817–826, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Yin, H. J. Gao, J. B. Qiu, and O. Kaynark, “Descriptor reduced-order sliding mode observers design for switched systems with sensor and actuator faults,” Automatica, vol. 76, pp. 282–292, 2017. [click]

    Article  MathSciNet  MATH  Google Scholar 

  16. Q. Y. Su and J. Zhao, “Stabilization of a class switched systems with state constraints,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1499–1510, 2011. [click]

    Article  MathSciNet  MATH  Google Scholar 

  17. D. Liberzon and A. S. Morse, “Basic problems in stability and design of switched systems,” IEEE Control Systems Magazine, vol. 19, no. 15, pp. 59–70, 1999.

    Article  MATH  Google Scholar 

  18. X. D. Zhao, L. X. Zhang, P. Shi, and M. Liu, “Stability of switched positive linear systems with average dwell time switching,” Automatica, vol. 48, no. 6, pp. 1132–1137, 2012.

    Article  MathSciNet  MATH  Google Scholar 

  19. H. Q. Wang, X. P. Liu, and P. Shi, “Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems,” IEEE Transactions on Cybernetics, vol. 47, no. 9, pp. 2568–2578, 2017.

    Article  Google Scholar 

  20. H. Q. Wang, W. J. Sun, and X. P. Liu, “Adaptive intelligent control for a class of non-affine nonlinear time-delay systems with dynamic uncertainties,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 7, pp. 1474–1485, 2017.

    Article  Google Scholar 

  21. Y. M. Li and S. C. Tong, “Adaptive fuzzy output-feedback stabilization control for a class of switched non-strictfeedback nonlinear systems,” IEEE Transactions on Cybernetics, vol. 47, no. 4, pp. 1007–1016, 2017.

    Article  Google Scholar 

  22. Y. M. Li, S. C. Tong, and T. S. Li, “Adaptive fuzzy outputfeedback control for output constrained nonlinear systems in the presence of input saturation,” Fuzzy Sets and Systems, vol. 248, pp. 138–155, 2014. [click]

    Article  MathSciNet  MATH  Google Scholar 

  23. Y. M. Li and S. C. Tong, “Adaptive fuzzy output constrained control design for multi-input multi-output stochastic non-strict-feedback nonlinear systems,” IEEE Transactions on Cybernetics, vol. 47, no. 12, pp. 4086–4095, 2017.

    Article  Google Scholar 

  24. D. Rosinova, V. Vesely, and V. Kucera, “A necessary and sufficient condition for static output feedback stabilizability of linear discrete-time systems,” Kybernetika, vol. 39, no. 4, pp. 447–459, 2003.

    MathSciNet  MATH  Google Scholar 

  25. C. A. R. Crusius and A. Trofino, “Sufficient LMI conditions for output feedback control problems,” IEEE Transaction Automation Control, vol. 44, no. 5, pp. 1053–1057, 1999. [click]

    Article  MathSciNet  MATH  Google Scholar 

  26. Y. Y. Cao, J. Lam, and Y. X. Sun, “Static output feedback stabilization: an ILMI approach,” Automatica, vol. 34, no. 12, pp. 1641–1645, 1998.

    Article  MATH  Google Scholar 

  27. H. J. Fang and Z. L. Lin, “Stability analysis for linear systems under state constraint,” IEEE Transaction on Automatic Control, vol. 49, no. 6, pp. 950–955, 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  28. X. D. Zhao, L. X. Zhang, P. Shi, and M. Liu, “Stability and stabilization of switched linear systems with modedependent average dwell time,” IEEE Transactions on Automatic Control, vol. 57, no. 7, pp. 1809–1815, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. Q. Y. Su and J. Zhao, “H ∞ control for a class of continuoustime switched systems with state constraints,” Asian Journal of Control, vol. 16, no. 2, pp. 451–460, 2013. [click]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Qingyu Su, Haichao Zhu & Jian Li

Authors
  1. Qingyu Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Haichao Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jian Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jian Li.

Additional information

Recommended by Associate Editor Huanqing Wang under the direction of Editor Myo Taeg Lim. This work was supported by the National Natural Science Foundation of China (61503071,61703091), Natural Science Foundation of Jilin Province (20180520211JH) and Science Research of Education Department of Jilin Province (201693, JJKH20170106KJ).

Qingyu Su received his B.Sc. degree in electrical automation in 2005, and his M.Sc. degree in control theory and application in 2008, both from Liaoning Technical University, China. He completed his Ph.D. degree in control theory and application in 2013 at Northeastern University, China. Now he is an Associate Professor at the School of Automation Engineering, Northeast Electric University, China. From October 2015 to October 2016, he was a visiting scholar at the Intelligent Systems and Biomedical Robotics Group (ISR), University of Portsmouth, UK. He has published 13 articles on SCI Journals and 8 papers on international conferences. His research interests include switched systems, nonlinear control systems and power systems.

Haichao Zhu received his B.Sc. degree in electrical engineering and automation in 2014 from Henan Polytechnic University, China. Now he is a master degree candidate at the School of Automation Engineering, Northeast Electric University, China. His research interests include switched systems and robust control.

Jian Li received her B.Sc. and M.Sc. degrees in electrical automation and control theory and application from the Liaoning Technical University, China in 2005 and 2008, respectively, and the Ph.D. degree in control theory and application from Northeast University, China in 2013. Currently, she is an Associate Professor in the School of Automation Engineering, Northeast Electric University, China. From July, 2015 to August, 2015, she was a visiting scholar at the Nonlinear Dynamics Group, Yeungnam University, South Korea. Her research interests include fault detection, robust control and micro-grid.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Su, Q., Zhu, H. & Li, J. Static Output Feedback Stabilization of a Class of Switched Linear Systems with State Constraints. Int. J. Control Autom. Syst. 16, 505–511 (2018). https://doi.org/10.1007/s12555-016-0800-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0800-5

Keywords

Search

Navigation