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Robust output feedback stabilization of nonlinear networked systems via a finite data-rate communication channel

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Abstract

This paper addresses a robust stabilization problem of a class of uncertain nonlinear systems using output measurements via a finite data-rate communication channel. The authors assumes that there exist an observer and a control law for the systems in the absence of any finite data-rate communication channel. Based on the observer and the control law, the authors constructs an encoder/decoder pair and provides a sufficient condition, including suitable sampling period and data rate, which will guarantee the stability of the closed-loop systems when a finite data-rate communication channel is introduced.

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References

  1. A. V. Savkin and R. J. Evans, Hybrid Dynamical Systems: Controller and Sensor Switching Problems, Birkhäuser, Boston, 2002.

    MATH  Google Scholar 

  2. A. S. Matveev and A. V. Savkin, Qualitative Theory of Hybrid Dynamical Systems, Birkhäuser, Boston, 2000.

    MATH  Google Scholar 

  3. H. Ishii and B. A. Francis, Limited Data Rate in Control Systems with Networks, Springer-Verlag, Berlin, 2002.

    MATH  Google Scholar 

  4. I. R. Petersen and A. V. Savkin, Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel, Proc. 40th IEEE Conf. Decision and Control, 2001: 304–309.

  5. V. N. Phat, J. Jiang, A. V. Savkin, and I. R. Petersen, Robust stabilization of linear uncertain discrete-time systems via a limited capacity communication channel, Systems & Control Letters, 2004, 53(5): 347–360.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. S. Matveev and A. V. Savkin, The problem of LQG optimal control via a limited capacity communication model, Systems & Control Letters, 2004, 53(1): 51–64.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. S. Matveev and A. V. Savkin, Estimation and Control over Communication Networks, Birkhäuser, Boston, 2009.

    MATH  Google Scholar 

  8. G. N. Nair, R. J. Evans, I. M. Y. Mareels, and W. Moran, Topological feedback entropy and nonlinear stabilization, IEEE Transactions on Automatic Control, 2004, 49(9): 1585–1597.

    Article  MathSciNet  Google Scholar 

  9. A. V. Savkin, Analysis and synthesis of networked control systems: Topological entropy, observability, robustness, and optimal control, Automatica, 2006, 42(1): 51–62.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Liberzon and J. P. Hespanha, Stabilization of nonlinear systems with limited information feedback, IEEE Transactions on Automatic Control, 2005, 50(6): 910–915.

    Article  MathSciNet  Google Scholar 

  11. C. De Persis, Nonlinear stabilization via encoded feedback: The case of integral ISS systems, Automatica, 2006, 42: 1813–1816.

    Article  MATH  Google Scholar 

  12. C. De Persis and A. Isidori, Stabilization by state feedback implies stabilizability by encoded state feedback, Systems & Control Letters, 2004, 53(3–4): 249–258.

    Article  MATH  MathSciNet  Google Scholar 

  13. C. De Persis, On stabilization of nonlinear systems under data rate constraints using output measurements, International Journal of Robust and Nonlinear Control, 2006, 16(6): 315–332.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. P. Gauthier and I. Kupca, Deterministic Observation Theory and Applications, Cambridge University Press, Cambridge, 2001.

    Book  MATH  Google Scholar 

  15. A. V. Savkin and T. M. Cheng, Detectability and output feedback stabilizability of nonlinear networked control systems, IEEE Transactions on Automatic Control, 2007, 52(4): 730–735.

    Article  MathSciNet  Google Scholar 

  16. T. M. Cheng and A. V. Savkin, Output feedback stabilization of nonlinear networked control systems with non-decreasing nonlinearities: A matrix inequalities approach, International Journal of Robust and Nonlinear Control, 2007, 17(5): 387–404.

    Article  MATH  MathSciNet  Google Scholar 

  17. R. Rajamani and Y. M. Cho, Existence and design of observers for nonlinear systems: Relation to distance to unobservability, International Journal of Control, 1998, 69(5): 717–731.

    Article  MATH  MathSciNet  Google Scholar 

  18. C. Aboky, G. Sallet, and J. C. Vivalda, Observers for lipschitz nonlinear systems, International Journal of Control, 2002, 75(3): 204–212.

    Article  MATH  MathSciNet  Google Scholar 

  19. B. Song and J. Hedrick, Observer-based dynamic surface control for a class of nonlinear systems: An LMI approach, IEEE Transactions on Automatic Control, 2004, 49(11): 1995–2001.

    Article  MathSciNet  Google Scholar 

  20. E. D. Sontag and A. Teel, Changing supply functions in input/state stable systems, IEEE Transactions on Automatic Control, 1995, 40(7): 1476–1478.

    Article  MATH  MathSciNet  Google Scholar 

  21. T. M. Cheng, V. Malyavej, and A. V. Savkin, Decentralized robust set-valued state estimation in networked multiple sensor systems, Computers and Mathematics with Applications, 2010, 59(8): 2636–2646.

    Article  MATH  MathSciNet  Google Scholar 

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Correspondence to Teddy M. Cheng.

Additional information

This work was supported by the Australian Research Council.

This paper was recommended for publication by Editor Jinhu LÜ.

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Cheng, T.M. Robust output feedback stabilization of nonlinear networked systems via a finite data-rate communication channel. J Syst Sci Complex 24, 1–13 (2011). https://doi.org/10.1007/s11424-011-8397-5

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  • DOI: https://doi.org/10.1007/s11424-011-8397-5

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