Skip to main content
SpringerLink
Log in

Stabilization for a Class of Discrete-time Switched Large-scale Systems with Parameter Uncertainties

  • Research Article
  • Published:
International Journal of Automation and Computing Aims and scope Submit manuscript

Abstract

The problem of robust stabilization for a class of discrete-time switched large-scale systems with parameter uncertainties and nonlinear interconnected terms is considered. By using state feedback and Lyapunov function technique, a decentralized switching control approach is put forward to guarantee the solutions of large-scale systems converge to the origin globally. A numerical example and a corresponding simulation result are utilized to verify the effectiveness of the presented approach.

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.

Similar content being viewed by others

References

  1. B. Zhou, G. R. Duan, Z. Lin. Approximation and monotonicity of the maximal invariant ellipsoid for discrete-time systems by bounded controls. IEEE Transactions on Automatic Control, vol. 55, no. 2, pp. 440–446, 2010.

    Article  MathSciNet  Google Scholar 

  2. B. Zhou, G. R. Duan, Z. Lin. A parametric periodic Lyapunov equation with application in semi-global stabilization of discrete-time periodic systems subject to actuator saturation. Automatica, vol. 47, no. 2, pp. 316–325, 2011.

    Article  MathSciNet  Google Scholar 

  3. Z. Zhang, Z. Zhang, H. Zhang, B. Zheng, H. R. Karimi. Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay. Journal of the Franklin Institute, vol. 351, no. 6, pp. 3457–3476, 2014.

    Article  MathSciNet  Google Scholar 

  4. Y. Zhang, C. Liu. Observer-based finite-time H∞ control of discrete-time Markovian jump systems. Applied Mathematical Modelling, vol. 37, no. 6, pp. 3748–3760, 2013.

    Article  MathSciNet  Google Scholar 

  5. Z. Zuo, H. Li, Y. Wang. New criterion for finite-time stability of linear discrete-time systems with time-varying delay. Journal of the Franklin Institute, vol. 350, no. 9, pp. 2745–2756, 2013.

    Article  MathSciNet  Google Scholar 

  6. B. Zhou, W. X. Zheng, G. R. Duan. Stability and stabilization of discrete-time periodic linear systems with actuator saturation. Automatica, vol. 47, no. 8, pp. 1813–1820, 2011.

    Article  MathSciNet  Google Scholar 

  7. B. Zhou. Analysis and design of discrete-time linear systems with nested actuator saturations. Systems and Control Letters, vol. 62, no. 10, pp. 871–879, 2013.

    Article  MathSciNet  Google Scholar 

  8. G. Zong, R. Wang, W. X. Zheng, L. Hou. Finite-time stabilization for a class of switched time-delay systems under asynchronous switching. Applied Mathematics and Computation, vol. 219, no. 11, pp. 5757–5771, 2013.

    Article  MathSciNet  Google Scholar 

  9. X. Zhao, Z. Yu, X. Yang, H. Li. Estimator design of discrete-time switched positive linear systems with average dwell time. Journal of the Franklin Institute, vol. 351, no. 1, pp. 579–588, 2014.

    Article  MathSciNet  Google Scholar 

  10. X. Yu, C. Wu, F. Liu, L. Wu. Sliding mode control of discrete-time switched systems with time-delay. Journal of the Franklin Institute, vol. 350, no. 1, pp. 19–33, 2013.

    Article  MathSciNet  Google Scholar 

  11. I. Malloci, J. Daafouz, C. Iung. Stability and stabilization of two time scale switched systems in discrete time. IEEE Transactions on Automatic Control, vol. 55, no. 6, pp. 1434–1438, 2010.

    Article  MathSciNet  Google Scholar 

  12. Z. Sun. Robust switching of discrete-time switched linear systems. Automatica, vol. 48, no. 1, pp. 239–242, 2012.

    Article  MathSciNet  Google Scholar 

  13. W. A. Zhang, L. Yu. Stability analysis for discrete-time switched time-delay systems. Automatica, vol. 45, no. 10, pp. 2265–2271, 2009.

    Article  MathSciNet  Google Scholar 

  14. D. W. Ding, G. H. Yang. H∞ static output feedback control for discrete-time switched linear systems with average dwell time. IET Control Theory and Applications, vol. 4, no. 3, pp. 381–390, 2010.

    Article  MathSciNet  Google Scholar 

  15. W. Xiang, J. Xiao. H∞ finite-time control for switched nonlinear discrete-time systems with norm-bounded disturbance. Journal of the Franklin Institute, vol. 348, no. 2, pp. 331–352, 2011.

    Article  MathSciNet  Google Scholar 

  16. X. Xu, G. Zhai, S. He. Some results on practical stabilizability of discrete-time switched affine systems. Nonlinear Analysis: Hybrid Systems, vol. 4, no. 1, pp. 113–121, 2010.

    MathSciNet  MATH  Google Scholar 

  17. V. N. Phat, K. Ratchagit. Stability and stabilization of switched linear discrete-time systems with interval timevarying delay. Nonlinear Analysis: Hybrid Systems, vol.5, no. 4, pp. 605–612, 2011.

    MathSciNet  MATH  Google Scholar 

  18. X. Dai, Y. Huang, M. Xiao. Periodically switched stability induces exponential stability of discrete-time linear switched systems in the sense of Markovian probabilities. Automatica, vol. 47, no. 7, pp. 1512–1519, 2011.

    Article  MathSciNet  Google Scholar 

  19. Y. Huang, J. Luo, T. Huang, M. Q. Xiao. The set of stable switching sequences for discrete-time linear switched systems. Journal of Mathematical Analysis and Applications, vol. 377, no. 2, pp. 732–743, 2011.

    Article  MathSciNet  Google Scholar 

  20. X. Zhang, J. Zhao. L2-gain analysis and anti-windup design of discrete-time switched systems with actuator saturation. International Journal of Automation and Computing, vol.9, no. 4, pp. 369–377, 2012.

    Article  Google Scholar 

  21. C. Sun, B. Fang, W. Huang. Existence of a common quadratic Lyapunov function for discrete switched linear systems with m stable subsystems. IET Control Theory and Applications, vol. 5, no. 3, pp. 535–537, 2011.

    Article  MathSciNet  Google Scholar 

  22. C. Sun, Y. Z. Liu. Robust state feedback stabilization for a class of uncertain switched systems. Control Theory & Applications, vol. 22, no. 5, pp. 794–798, 2005. (in Chinese)

    Google Scholar 

  23. C. Sun. Decentralized control for discrete-time switched large-scale linear systems. The 2nd International Conference on Intelligent Control and Information Processing, Harbin, China, pp. 325–328, 2011.

    Google Scholar 

  24. X. L. Liang, M. Z. Hou, G. R. Duan. Output feedback stabilization of switched stochastic nonlinear systems under arbitrary switchings. International Journal of Automation and Computing, vol. 10, no. 6, pp. 571–577, 2013.

    Article  Google Scholar 

  25. C. H. Lien, K. W. Yu, Y. J. Chung, H. C. Chang, J. D. Chen. Switching signal design for global exponential stability of uncertain switched nonlinear systems with timevarying delay. Nonlinear Analysis: Hybrid Systems, vol.5, no. 1, pp. 10–19, 2011.

    MathSciNet  MATH  Google Scholar 

  26. W. H. Chen, W. X. Zheng. Delay-independent minimum dwell time for exponential stability of uncertain switched delay systems. IEEE Transactions on Automatic Control, vol. 55, no. 10, pp. 2406–2413, 2010.

    Article  MathSciNet  Google Scholar 

  27. Z. Xiang, Q. Chen. Robust reliable control for uncertain switched nonlinear systems with time delay under asynchronous switching. Applied Mathematics and Computation, vol. 216, no. 3, pp. 800–811, 2010.

    Article  MathSciNet  Google Scholar 

  28. H. Xu, K. L. Teo. Robust stabilization of uncertain impulsive switched systems with delayed control. Computers and Mathematics with Applications, vol. 56, no. 1, pp. 63–70, 2008.

    Article  MathSciNet  Google Scholar 

  29. I. R. Petersen. A stabilization algorithm for a class of uncertain linear systems. Systems and Control Letters, vol.8, no. 4, pp. 351–357, 1987.

    Article  MathSciNet  Google Scholar 

  30. Y. Zhang, G. R. Duan. Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems. Journal of Systems Engineering and Electronics, vol. 18, no. 4, pp. 846–851, 2007.

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Scientific Research Project of Liaoning Provincial Education Department, China (No. L2013229) and the Mathematics Subject Development Project of Shenyang Jianzhu University, China (No. XKHY-78).

Author information

Authors and Affiliations

  1. School of Science, Shenyang Jianzhu University, Shenyang, 110168, China

    Chang-Chun Sun

Authors
  1. Chang-Chun Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chang-Chun Sun.

Additional information

Recommended by Associate Editor Min Wu

Chang-Chun Sun received the Ph.D. degree from Harbin Institute of Technology, China in 2012. He is currently an associate professor at School of Science, Shenyang Jianzhu University, China.

His research interests include analysis, control and simulations of nonlinear dynamical systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sun, CC. Stabilization for a Class of Discrete-time Switched Large-scale Systems with Parameter Uncertainties. Int. J. Autom. Comput. 16, 543–552 (2019). https://doi.org/10.1007/s11633-016-0966-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11633-016-0966-6

Keywords

Search

Navigation