Skip to main content
SpringerLink
Log in

Decentralized \(\mathscr{H}_{\infty }\) Sampled-Data Control for Continuous-Time Large-Scale Networked Nonlinear Systems

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

Abstract

The decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem is investigated for a class of continuous-time large-scale networked nonlinear systems with interconnection. Each nonlinear subsystem in the considered large-scale system is represented by a Takagi–Sugeno model and is closed by a communication channel with transformed time delay. Our objective is to design a decentralized sampled-data fuzzy controller such that the resulting fuzzy control system is asymptotically stable with an \({\mathscr{H}}_{\infty }\) performance. Firstly, using an input delay approach, the sampled-data control system is formulated into the system with time-varying delay, and a two-term approximation method is proposed such that the delayed system is reformulated into an interconnected framework with input and output. Then, we introduce a Lyapunov–Krasovskii functional that all Lyapunov matrices are no longer required to be positive definite. Combined with the scaled small gain theorem, the less conservative solutions to the decentralized \({\mathscr{H}}_{\infty }\) sampled-data control problem for the considered system are derived in the form of linear matrix inequalities. Finally, the effectiveness of the proposed methods is illustrated by two numerical examples.

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

Similar content being viewed by others

References

  1. Tanaka, T., Wang, H.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)

    Book  Google Scholar 

  2. Li, Y., Tong, S., Li, T.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45(10), 2299–2308 (2015)

    Article  MathSciNet  Google Scholar 

  3. Wang, Y., Zhang, H., Zhang, J., Wang, Y.: An SOS-based observer design for discrete-time polynomial fuzzy systems. Int. J. Fuzzy Syst. 17(1), 94–104 (2015)

    Article  MathSciNet  Google Scholar 

  4. Qiu, J., Ding, S.X., Gao, H., Yin, S.: Fuzzy-model-based reliable static output feedback \(\fancyscript {H}_{\infty }\) control of nonlinear hyperbolic PDE systems. IEEE Transactions on Fuzzy Systems. IEEE Trans. Fuzzy Syst. (2015). doi: 10.1109/TFUZZ.2015.2457934

  5. Tong, S., Li, Y.: Adaptive fuzzy output feedback control of MIMO nonlinear systems with unknown dead-zone inputs. IEEE Trans. Fuzzy Syst. 21(1), 134–146 (2013)

    Article  MathSciNet  Google Scholar 

  6. Qiu, J., Feng, G., Gao, H.: Observer-based piecewise affine output feedback controller synthesis of continuous-time T–S fuzzy affine dynamic systems using quantized measurements. IEEE Trans. Fuzzy Syst. 20(6), 1046–1062 (2012)

    Article  Google Scholar 

  7. Siljak, D.: Large-Scale Dynamic Systems: Stability and Structure. Elsevier/North-Holland, New York (1978)

    MATH  Google Scholar 

  8. Bakule, L.: Decentralized control: status and outlook. Annu. Rev. Control 38(1), 71–80 (2014)

    Article  Google Scholar 

  9. Mahmoud, M., Qureshi, A.: Decentralized sliding-mode output-feedback control of interconnected discrete-delay systems. Automatica 48(5), 808–814 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Yu, G., Zhang, H., Huang, Q., Dang, C.: New delay-dependent stability analysis for fuzzy time-delay interconnected systems. Int. J. Gen. Syst. 42(7), 739–753 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, Y., Tong, S., Li, T.: Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems. IEEE Trans. Cybern. 45(1), 138–149 (2015)

    Article  Google Scholar 

  12. Li, Y., Tong, S., Liu, Y., Li, T.: Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small-gain approach. IEEE Trans. Cybern. 22(1), 164–176 (2014)

    Google Scholar 

  13. Tong, S., Li, Y., Zhang, H.: Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays. IEEE Trans. Neural Netw. 22(7), 1073–1086 (2011)

    Article  Google Scholar 

  14. Wu, H.: Decentralized adaptive robust control for a class of large-scale systems including delayed state perturbations in the interconnections. IEEE Trans. Autom. Control 47(10), 1745–1751 (2002)

    Article  MathSciNet  Google Scholar 

  15. Zhang, H., Yu, G., Zhou, C., Dang, C.: Delay-dependent decentralized \(\fancyscript {H}_{\infty }\) filtering for fuzzy interconnected systems with time-varying delay based on Takagi–Sugeno fuzzy model. IET Control Appl. 7(5), 720–729 (2013)

    Article  MathSciNet  Google Scholar 

  16. Zhong, Z., Fu, S., Hayat, T., Alsaadi, F., Sun, G.: Decentralized piecewise \(\fancyscript {H}_{\infty }\) fuzzy filtering design for discrete-time large-scale nonlinear systems with time-varying delay. J. Frankl. Inst. 352(9), 3782–3807 (2015)

    Article  MathSciNet  Google Scholar 

  17. Zhang, H., Zhong, H., Dang, C.: Delay-dependent decentralized \(\fancyscript {H}_{\infty }\) filtering for discrete-time nonlinear interconnected systems with time-varying delay based on the T–S fuzzy model. IEEE Trans. Fuzzy Syst. 20(3), 431–443 (2012)

    Article  Google Scholar 

  18. Tong, S., Huo, B., Li, Y.: Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans. Fuzzy Syst. 22(1), 1–15 (2014)

    Article  Google Scholar 

  19. Tseng, C.: A novel approach to \(\fancyscript {H}_{\infty }\) decentralized fuzzy-observer-based fuzzy control design for nonlinear interconnected systems. IEEE Trans. Fuzzy Syst. 16(5), 1337–1350 (2008)

    Article  Google Scholar 

  20. Zhu, Y., Zhang, L., Zheng, W.: Distributed \(\fancyscript {H}_{\infty }\) filtering for a class of discrete-time Markov jump Lure systems with redundant channels. IEEE Trans. Ind. Electron. (2015) doi: 10.1109/TIE.2015.2499169

  21. Zhu, Y., Zhang, L., Basin, M.: Nonstationary \(\fancyscript {H}_{\infty }\) dynamic output feedback control for discrete-time Markov iump linear systems with actuator and sensor saturations. Int. J. Robust Nonlinear Control (2015). doi: 10.1002/rnc.3348

  22. Fridman, E.: A refined input delay approach to sampled-data control. Automatica 46(2), 421–427 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Zhang, J., Knopse, C., Tsiotras, P.: Stability of time-delay systems: equivalence between Lyapunov and scaled small-gain conditions. IEEE Trans. Autom. Control 46(3), 482–486 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  24. Gu, K., Kharitonov, V., Chen, J.: Stability of Time-Delay Systems. Birkhauser, Boston (2003)

    Book  MATH  Google Scholar 

  25. Jiang, X., Han, Q., Yu, X.: Stability criteria for linear discrete-time systems with interval-like time-varying delay. In: Proceedings of the 2005 IEEE conference on American control, vol. 4, pp. 2817–2822 (2005)

  26. Gu, K., Zhang, Y., Xu, S.: Small gain problem in coupled differential-difference equations, time-varying delays, and direct Lyapunov method. Int. J. Robust Nonlinear Control 21(4), 429–451 (2011)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors are grateful to the Editor-in-Chief, the Associate Editor, and anonymous reviewers for their constructive comments based on which the presentation of this paper has been greatly improved. This work was supported in part by the Natural Science Foundation (2015J01275) of the Science and Technology Agency, Fujian, and the National Science Council of Taiwan under Grant NSC98-2221-E-155-059-MY3, and the Science and Technology-Planned Project (3502Z20143034) of Xiamen, and the Foreign Science and Technology Special Cooperation (E201401400) and (E201400900) of Xiamen University of Technology, and the Natural Foundation Pre-Research Project (XYK201402) of Xiamen University of Technology, China.

Author information

Authors and Affiliations

  1. School of Electrical Engineering and Automation, Xiamen University of Technology, Xiamen, 361024, People’s Republic of China

    Jing Zhao & Jiangyin Huang

  2. Department of Electrical Engineering, Yuan Ze University, Chung-Li, Tao-Yuan 320, Taiwan, Republic of China

    Jing Zhao

  3. School of Information Science and Engineering, Xiamen University, Xiamen, People’s Republic of China

    Chih-Min Lin

  4. Department of Electrical Engineering and Innovation Center for Big Data and Digital Convergence, Yuan Ze University, Chung-Li, Tao-Yuan 320, Taiwan, Republic of China

    Chih-Min Lin

Authors
  1. Jing Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chih-Min Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiangyin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Jing Zhao or Chih-Min Lin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, J., Lin, CM. & Huang, J. Decentralized \(\mathscr{H}_{\infty }\) Sampled-Data Control for Continuous-Time Large-Scale Networked Nonlinear Systems. Int. J. Fuzzy Syst. 19, 504–515 (2017). https://doi.org/10.1007/s40815-016-0140-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0140-x

Keywords

Search

Navigation