Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
SpringerLink
Log in

Weighted \(\mathbf{H}_\infty\) Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

In this paper, the issues about weighted \(H_\infty\) performance analysis and \(H_\infty\) control for the stochastic switched nonlinear systems (SSNSs) with multiplicative noise are investigated. The mode-dependent average dwell time (MDADT) method is used to deal with the switching in different modes. Firstly, we get a sufficient condition to show that the considered system with all stable subsystems achieves the exponential stability in mean square sense and a specified weighted \(H_\infty\) performance, which is extended to the case that both stable and unstable subsystems coexist in terms of second-order Hamilton-Jacobi inequalities (HJIs). Then, by using Takagi-Sugeno (T-S) fuzzy approach, the \(H_\infty\) controller for SSNSs is designed via solving a set of linear matrix inequalities (LMIs). Finally, an example is supplied to illustrate the effectiveness of our results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

References

  1. Wu, J.: Stabilizing controllers design for switched nonlinear systems in strict-feedback form. Automatica 45(4), 1092–1096 (2009)

    Article  MathSciNet  Google Scholar 

  2. Wu, J.: Feedback stabilization for multi-input switched nonlinear systems: two subsystems case. IEEE Trans. Autom. Control 53(4), 1037–1042 (2008)

    Article  Google Scholar 

  3. Zhai, D., An, L., Dong, J., Zhang, Q.: Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching. IEEE Trans. Fuzzy. Syst. 26(2), 585–597 (2018)

    Article  Google Scholar 

  4. Baldi, S., Xiang, W.: Reachable set estimation for switched linear systems with dwell-time switching. Nonlinear. Anal-Hybri. 29, 20–33 (2018)

    Article  MathSciNet  Google Scholar 

  5. Yang, H., Jiang, B., Zhang, H.: Stabilization of non-minimum phase switched nonlinear systems with application to multi-agent systems. Syst. Control. Lett. 61(10), 1023–1031 (2012)

    Article  MathSciNet  Google Scholar 

  6. Li, Y., Sui, S., Tong, S.: Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics. IEEE Trans. Cybern. 47(2), 403–414 (2017)

    Google Scholar 

  7. Wei, J., Zhi, H., Liu, K., Mu, X.: Stability of mode-dependent linear switched singular systems with stable and unstable subsystems. J. Frankl. Inst. 356(5), 3102–3114 (2019)

    Article  MathSciNet  Google Scholar 

  8. Luo, J., Tian, W., Zhong, S., Shi, K., Wang, W.: Non-fragile asynchronous event-triggered control for uncertain delayed switched neural networks. Nonlinear. Anal-Hybri. 29, 54–73 (2018)

    Article  MathSciNet  Google Scholar 

  9. Xia, Z., Li, J.: Switching fuzzy filtering for nonlinear stochastic delay systems using piecewise Lyapunov-Krasovskii function. Int. J. Fuzzy. Syst. 14(4), 530–539 (2012)

    MathSciNet  Google Scholar 

  10. Allerhand, L.I., Shaked, U.: Robust switching-based fault tolerant control. IEEE Trans. Autom. Control 60(8), 2272–2276 (2015)

    Article  MathSciNet  Google Scholar 

  11. Liang, J., Wu, B., Wang, Y., Niu, B., Xie, X.: Input-output finite-time stability of fractional-order positive switched systems. Circ. Syst. Signal. Pr. 38(4), 1619–1638 (2019)

    Article  MathSciNet  Google Scholar 

  12. Yang, D., Li, X., Shen, J., Zhou, Z.: State-dependent switching control of delayed switched systems with stable and unstable modes. Math. Method. Appl. Sci. 41(16), 6968–6983 (2018)

    Article  MathSciNet  Google Scholar 

  13. Yang, H., Jiang, B., Cocquemport, V.: A survey of results and perspectives on stabilization of switched nonlinear systems with unstable modes. Nonlinear. Anal-Hybri. 13, 45–60 (2014)

    Article  MathSciNet  Google Scholar 

  14. Zhang, L., Cheng, D., Liu, J.B.: Stabilization of switched linear systems. Asian. J. Control 5(4), 476–483 (2003)

    Article  Google Scholar 

  15. Haspanha, J. P., Morse, A. S.: Stability of switched systems with average dwell time, In: Proceddings of the 38th IEEE Conference on Decision and Control, Phoenix, USA, 2655-2660 (1999)

  16. Zhao, X., Zhang, L., Shi, P., Liu, M.: Stability and stabilization of switched linear systems with mode-dependent average dwell time. IEEE Trans. Autom. Control 57(7), 1809–1815 (2012)

    Article  MathSciNet  Google Scholar 

  17. Zhao, X., Liu, H., Wang, Z.: Weighted \(H_\infty\) performance analysis of switched linear systems with mode-dependent average dwell time. Int. J. Syst. Sci. 44(11), 2130–2139 (2013)

    Article  MathSciNet  Google Scholar 

  18. Xie, D., Zhang, H., Zhang, H., Wang, B.: Exponential stability of switched systems with unstable subsystems: a mode-dependent average dwell time approach. Circ. Syst. Signal. Pr. 32, 3093–3105 (2013)

    Article  MathSciNet  Google Scholar 

  19. Shi, S., Fei, Z., Li, J.: Finite-time \(H_\infty\) control of switched systems with mode-dependent average dwell time. J. Frankl. Inst. 353, 221–234 (2016)

    Article  MathSciNet  Google Scholar 

  20. Huang, R., Lin, Y., Ge, S.S., Lin, Z.: \(H_\infty\) stabilisation of switched linear stochastic systems under dwell time constraints. Int. J. Control 85(9), 1209–1217 (2012)

    Article  MathSciNet  Google Scholar 

  21. Jiang, X., Tian, S., Zhang, W.: Pareto optimal strategy for linear stochastic systems with \(H_\infty\) constraint in finite horizon. Inf. Sci. 512, 1103–1117 (2020)

    Article  MathSciNet  Google Scholar 

  22. Chen, A., Shen, M.: A new method to reliable \(H_\infty\) control of nonlinear stochastic systems with actuator faults. Int. J. Fuzzy Syst. 21(1), 60–71 (2019)

    Article  MathSciNet  Google Scholar 

  23. Yang, Y., Zhao, J., Xia, J., Zhuang, G., Zhang, W.: Multiobjective optimization control for uncertain nonlinear stochastic system with state-delay. Int. J. Fuzzy. Syst. 21(1), 72–83 (2019)

    Article  MathSciNet  Google Scholar 

  24. Xing, X., Liu, Y., Niu, B.: \(H_\infty\) control for a class of stochastic switched nonlinear systems: an average dwell time method. Nonlinear. Anal-Hybri. 19, 198–208 (2016)

    Article  MathSciNet  Google Scholar 

  25. Jiang, X., Tian, S., Zhang, T., Zhang, W.: Weighted \(H_\infty\) performance analysis of nonlinear stochastic switched systems with state dependent noise: a mode-dependent average dwell time method, In: Proceedings of the 8th Internathinal Conference on Infromation Science and Technology, Spain, 314–320 (2018)

  26. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man, Cybern., Syst., 15(1), 116–132 (1985)

    Article  Google Scholar 

  27. Tong, S., Sun, K., Sui, S.: Observer-based adaptive fuzzy decentralized optimal control design for strict-feedback nonlinear large-scale systems. IEEE Trans. Fuzzy Syst., 26(2), 569–584 (2018)

    Article  Google Scholar 

  28. Sun, W., Su, S.F., Wu, Y., Xia, J., Nguyen, V.T.: Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2018.2890256

    Article  Google Scholar 

  29. Zhang, W., Pan, Z., Li, Y.: \(H_\infty\) filtering for general delayed nonlinear stochastic systems with Markov jumps. Int. J. Fuzzy. Syst. 19(6), 1989–2002 (2017)

    Article  MathSciNet  Google Scholar 

  30. Su, X., Shi, P., Wu, L., Song, Y.: Fault detection filtering for nonlinear switched stochastic systems. IEEE Trans. Autom. Control 61(5), 1310–1315 (2016)

    Article  MathSciNet  Google Scholar 

  31. Has’minskii, R.: Stochastic Stability of Differential Equations. Sijthoff and Noordhoff, Alphen (1980)

    Book  Google Scholar 

  32. Pierre, W. R. S.: Practical dwell times for switched system stability with smart grid application. Masters Theses, https://scholarsmine.mst.edu/masters_theses/7836, (2018)

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

    Article  MathSciNet  Google Scholar 

  34. Chen, B.S., Tseng, C.S., Uang, H.J.: Robustness design of nonlinear dynamic systems via fuzzy linear control. IEEE Trans. Fuzzy. Syst. 7(5), 571–585 (1999)

    Article  Google Scholar 

  35. Peng, Z., Wang, J., Wang, D.: Distributed maneuvering of autonomous surface vehicles based on neurodynamic optimization and fuzzy approximation. IEEE Trans. Control Syst. Technol. 26(3), 1083–1090 (2018)

    Article  MathSciNet  Google Scholar 

  36. Li, Y., Liu, L., Feng, G.: Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems. Automatica 89, 325–332 (2018)

    Article  MathSciNet  Google Scholar 

  37. Li, Y., Tong, S.: Adaptive neural networks prescribed performance control design for switched interconnected uncertain nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(7), 3059–3068 (2018)

    Article  MathSciNet  Google Scholar 

  38. Zhang, W., Xie, L., Chen, B.S.: Stochastic \(H_2/H_\infty\) Control: A Nash Game Approach. CRC Press, (2017)

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (61374104, 61773170, 61873099), the Key Laboratory of Autonomous Systems and Networked Control, and the Natural Science Foundation of Guangdong Province of China (2016A030313505).

Author information

Authors and Affiliations

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou, 510640, Guangdong Province, People’s Republic of China

    Xiushan Jiang & Senping Tian

  2. College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao, 266590, Shandong Province, People’s Republic of China

    Weihai Zhang

Authors
  1. Xiushan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Senping Tian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Weihai Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Senping Tian.

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

Jiang, X., Tian, S. & Zhang, W. Weighted \(\mathbf{H}_\infty\) Performance Analysis of Nonlinear Stochastic Switched Systems: A Mode-Dependent Average Dwell Time Method. Int. J. Fuzzy Syst. 22, 1454–1467 (2020). https://doi.org/10.1007/s40815-020-00864-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-020-00864-3

Keywords

Search

Navigation