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Characterization of Decentralized and Quotient Fixed Modes Via Graph Theory

  • Somayeh Sojoudi
  • Javad Lavaei
  • Amir G. Aghdam
Chapter

Abstract

Many real-world systems can be envisaged as the interconnected systems consisting of a number of subsystems. Normally, the desirable control structure for this class of systems is decentralized, which comprises a set of local controllers for the subsystems [1, 2, 3, 4, 5, 6]. Decentralized control theory has found applications in large space structure, communication networks, power systems, etc. [7, 8, 9, 10]. More recently, simultaneous stabilization of a set of decentralized systems and decentralized periodic control design are investigated in [11, 12].

Keywords

Bipartite Graph Zero Vector Interconnected System Local Controller Algebraic Characterization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    S. H. Wang and E. J. Davison, “On the stabilization of decentralized control systems,” IEEE Transactions on Automatic Control, vol. 18, no. 5, pp. 473–478, 1973.MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    E. J. Davison and T. N. Chang, “Decentralized stabilization and pole assignment for general proper systems,” IEEE Transactions on Automatic Control, vol. 35, no. 6, pp. 652–664, 1990.MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    J. Lavaei and A. G. Aghdam, “Elimination of fixed modes by means of high-performance constrained periodic control,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, pp. 4441–4447, 2006.Google Scholar
  4. 4.
    D. D. Šiljak, Decentralized control of complex systems, Cambridge: Academic Press, 1991.Google Scholar
  5. 5.
    D. D. Šiljak and A. I. Zecevic, “Control of large-scale systems: Beyond decentralized feedback,” Annual Reviews in Control, vol. 29, no. 2, pp. 169–179, 2005.CrossRefGoogle Scholar
  6. 6.
    J. Lavaei and A. G. Aghdam, “A necessary and sufficient condition for the existence of a LTI stabilizing decentralized overlapping controller,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, pp. 6179–6186, 2006.Google Scholar
  7. 7.
    G. Inalhan, D. M. Stipanovic, and C. J. Tomlin, “Decentralized optimization with application to multiple aircraft coordination,” in Proceedings of 41st IEEE Conference on Decision and Control, Vegas, NV., pp. 1147–1155, 2002.Google Scholar
  8. 8.
    J. Lavaei, A. Momeni and A. G. Aghdam, “High-performance decentralized control for formation flying with leader-follower structure,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, pp. 5947–5954, 2006.Google Scholar
  9. 9.
    J. Lavaei and A. G. Aghdam, “Decentralized control design for interconnected systems based on a centralized reference controller,” in Proceedings of 45th IEEE Conference on Decision and Control, San Diego, CA, pp. 1189–1195, 2006.Google Scholar
  10. 10.
    S. S. Stankovic, M. J. Stanojevic, and D. D. Šiljak, “Decentralized overlapping control of a platoon of vehicles,” IEEE Transactions on Control Systems Technology, vol. 8, no. 5, pp. 816–832, 2000.CrossRefGoogle Scholar
  11. 11.
    J. Lavaei and A. G. Aghdam, “Optimal periodic feedback design for continuous-time LTI systems with constrained control structure,” International Journal of Control, vol. 80, no. 2, pp. 220–230, 2007.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    J. Lavaei and A. G. Aghdam, “Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions,” Automatica, vol. 43, no. 2, pp. 274–280, 2007.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    B. L. O. Anderson and D. J. Clements, “Algebraic characterizations of fixed modes in decentralized systems,” Automatica, vol. 17, no. 5, pp. 703–712, 1981.MathSciNetCrossRefGoogle Scholar
  14. 14.
    B. L. O. Anderson, “Transfer function matrix description of decentralized fixed modes,” IEEE Transactions on Automatic Control, vol. 27, no. 6, pp. 1176–1182, 1982.MATHCrossRefGoogle Scholar
  15. 15.
    E. J. Davison and S. H. Wang, “A characterization of decentralized fixed modes in terms of transmission zeros,” IEEE Transactions on Automatic Control, vol. 30, no. 1, pp. 81–82, 1985.MathSciNetMATHCrossRefGoogle Scholar
  16. 16.
    Z. Gong and M. Aldeen, “On the characterization of fixed modes in decentralized control,” IEEE Transactions on Automatic Control, vol. 37, no. 7, pp. 1046–1050, 1992.MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Z. Gong and M. Aldeen, “Stabilization of decentralized control systems,” Journal of Mathematical Systems, Estimation, and Control, vol. 7, no. 1, pp. 1–16, 1997.MathSciNetGoogle Scholar

Copyright information

© Springer US 2011

Authors and Affiliations

  • Somayeh Sojoudi
    • 1
  • Javad Lavaei
    • 1
  • Amir G. Aghdam
    • 2
  1. 1.Control & Dynamical Systems Dept.California Institute of TechnologyPasadenaUSA
  2. 2.Dept. Electrical & Computer EngineeringConcordia UniversityMontreal QuébecCanada

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