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

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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.

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  1. 1

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

  2. 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

  3. 3

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

  4. 4

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

  5. 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

  6. 6

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

  7. 7

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

  8. 8

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

  9. 9

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

  10. 10

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

  11. 11

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

  12. 12

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

  13. 13

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

  14. 14

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

  15. 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

  16. 16

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

  17. 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

  18. 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

  19. 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

  20. 20

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

  21. 21

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

  22. 22

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

  23. 23

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

  24. 24

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

  25. 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

  26. 26

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

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

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Correspondence to Zhike Wang.

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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

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  • large scale networked system
  • time delay
  • robust stability
  • integral quadratic constraints
  • linear matrix inequalities