Skip to main content
Log in

IQC based robust stability verification for a networked system with communication delays

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

In this paper, we consider robust stability analysis of a networked system with uncertain communication delays. Each of its subsystems can have different dynamics, and interconnections among its subsystems are arbitrary. It is assumed that there exists an uncertain but constant delay in each communication channel. Using the so called integral quadratic constraint (IQC) technique, a sufficient robust stability condition is derived utilizing a sparseness assumption of the interconnections, and a set of decoupled robustness conditions are further derived which depend only on parameters of each subsystem, the subsystem connection matrix (SCM) and the selected IQC multipliers. These characteristics result in an evident improvement of computational efficiency for robustness verification of the networked system with delay uncertainties, which is illustrated by some numerical results.

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

Access this article

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.

Similar content being viewed by others

References

  1. D’Andrea R, Dullerud G E. Distributed control design for spatially interconnected systems. IEEE Trans Automat Contr, 2003, 48: 1478–1495

    Article  MathSciNet  Google Scholar 

  2. Langbort C, Chandra R S, D’Andrea R. Distributed control design for systems interconnected over an arbitrary graph. IEEE Trans Automat Contr, 2004, 49: 1502–1519

    Article  MathSciNet  Google Scholar 

  3. Zhou T. On the stability of spatially distributed systems. IEEE Trans Automat Contr, 2008, 53: 2385–2391

    Article  MathSciNet  Google Scholar 

  4. Fang H, Antsaklis P J. Distributed control with integral quadratic constraints. In: Proceedings of the 17th IFAC World Congress, Seoul, 2008. 574–580

    Google Scholar 

  5. Andersen M S, Pakazad S K, Hansson A, et al. Robust stability analysis of sparsely interconnected uncertain systems. IEEE Trans Automat Contr, 2014, 59: 2151–2156

    Article  MathSciNet  Google Scholar 

  6. Zhou T, Zhang Y. On the stability and robust stability of networked dynamic systems. IEEE Trans Automat Contr, 2016, 61: 1595–1600

    Article  MathSciNet  Google Scholar 

  7. Megretski A, Treil S. Power distribution inequalities in optimization and robustness of uncertain systems. J Math Syst, 1993, 3: 301–319

    MathSciNet  MATH  Google Scholar 

  8. Megretski A, Rantzer A. System analysis via integral quadratic constraints. IEEE Trans Automat Contr, 1997, 42: 819–830

    Article  MathSciNet  Google Scholar 

  9. Kao C Y, Rantzer A. Stability analysis of systems with uncertain time-varying delays. Automatica, 2007, 43: 959–970

    Article  MathSciNet  Google Scholar 

  10. Kao C Y. On stability of discrete-time LTI systems with varying time delays. IEEE Trans Automat Contr, 2012, 57: 1243–1248

    Article  MathSciNet  Google Scholar 

  11. Pfifer H, Seiler P. Integral quadratic constraints for delayed nonlinear and parameter-varying systems. Automatica, 2015, 56: 36–43

    Article  MathSciNet  Google Scholar 

  12. Seiler P. Stability analysis with dissipation inequalities and integral quadratic constraints. IEEE Trans Automat Contr, 2015, 60: 1704–1709

    Article  MathSciNet  Google Scholar 

  13. Fridman E, Shaked U. An improved stabilization method for linear time-delay systems. IEEE Trans Automat Contr, 2002, 47: 1931–1937

    Article  MathSciNet  Google Scholar 

  14. Kharitonov P L, Zhabko A P. Lyapunov-Krasovskii approach to the robust stability analysis of time-delay systems. Automatica, 2003, 39: 15–20

    Article  MathSciNet  Google Scholar 

  15. Summers E, Arcak M, Packard A. Delay robustness of interconnected passive systems: an integral quadratic constraint approach. IEEE Trans Automat Contr, 2013, 58: 712–724

    Article  MathSciNet  Google Scholar 

  16. Massioni P, Verhaegen M. Distributed control for identical dynamically coupled systems: a decomposition approach. IEEE Trans Automat Contr, 2009, 54: 124–135

    Article  MathSciNet  Google Scholar 

  17. Eichler A, Hoffmann C,Werner H. Robust stability analysis of interconnected systems with uncertain time-varying time delays via IQCs. In: Proceedings of the 52nd IEEE Conference on Decision and Control, Florence, 2013. 2799–2804

    Chapter  Google Scholar 

  18. Eichler A, Werner H. Improved IQC description to analyze interconnected systems with time-varying time-delays. In: Proceedings of American Control Conference, Chicago, 2015. 5402–5407

    Google Scholar 

  19. Wang Z K, Zhou T. Robust stability analysis of networked dynamic systems with uncertain communication delays. In: Proceedings of the 36th Chinese Control Conference, Dalian, 2017. 7684–7689

    Google Scholar 

  20. Willems J. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans Automat Contr, 1971, 16: 621–634

    Article  MathSciNet  Google Scholar 

  21. Rantzer A. On the Kalman-Yakubovich-Popov lemma. Syst Control Lett, 1996, 28: 7–10

    Article  MathSciNet  Google Scholar 

  22. Zhou T. Coordinated one-step optimal distributed state prediction for a networked dynamical system. IEEE Trans Automat Contr, 2013, 58: 2756–2771

    Article  MathSciNet  Google Scholar 

  23. Zhou T. On the controllability and observability of networked dynamic systems. Automatica, 2015, 52: 63–75

    Article  MathSciNet  Google Scholar 

  24. Zhou K M, Doyle J C, Glover K. Robust and Optimal Control. Upper Saddle River: Prentice-Hall, 1996. 239–260

    Google Scholar 

  25. Andersen M S, Hansson A, Pakazad S K, et al. Distributed robust sability analysis of interconnected uncertain systems. In: Proceedings of the 51st IEEE Conference on Decision and Control, Maui, 2012. 1548–1553

    Google Scholar 

  26. Benson S J, Ye Y. DSDP5 User Guide-Software for Semiderfinite Programming. Technical Report ANL/MCS-TM-277. 2005

    Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573209, 61733008).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zhike Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Z., Zhou, T. IQC based robust stability verification for a networked system with communication delays. Sci. China Inf. Sci. 61, 122201 (2018). https://doi.org/10.1007/s11432-017-9318-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-017-9318-2

Keywords

Navigation