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Asymptotic methods in stability analysis and control

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Stability and Stabilization of Nonlinear Systems

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 246))

Abstract

Systems depending on a small parameter are considered, and the interplay between convergence results for trajectories and stability properties is investigated. Under a continuity assumption for solutions, practical and exponential stability results are obtained. The presented results are useful for constructive stabilization of control systems and robustness analysis

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References

  1. D. Aeyels and J. Peuteman, On exponential stability of nonlinear time-varying differential equations. Automatica 35:1091–1100, 1999

    Article  MATH  MathSciNet  Google Scholar 

  2. P. Hartman, Ordinary Differential Equations, 2nd edn. Birkhäuser, 1982.

    Google Scholar 

  3. H.K. Khalil, Nonlinear Systems, 2nd edn. Prentice-Hall, 1996.

    Google Scholar 

  4. R.T. M’Closkey, An averaging theorem for time-periodic degree zero homogeneous differential equations. Systems and Control Letters 32:179–183, 1997.

    Article  MathSciNet  Google Scholar 

  5. R.T. M’Closkey and P. Morin, Time-varying homogeneous feedback: design tools for the exponential stabilization of systems with drift. International Journal of Control 71:837–869, 1998.

    Article  MathSciNet  Google Scholar 

  6. R.T. M’Closkey and R.M. Murray, Nonholonomic Systems and Exponential Convergence: Some Analysis Tools. In: Proceedings of the 32th IEEE Conference on Decision and Control 1993 (CDC’93), 943–948, 1993.

    Google Scholar 

  7. L. Moreau and D. Aeyels, Stability for Homogeneous Flows Depending on a Small Parameter. In: Proceedings of IFAC Nonlinear Control Systems Design Symposium 1998 (NOLCOS’98), 488–493, 1998.

    Google Scholar 

  8. L. Moreau and D. Aeyels, Practical Stability for Systems Depending on a Small Parameter. In: Proceedings of the 37th IEEE Conference on Decision and Control 1998 (CDC’98), 1428–1433, 1998.

    Google Scholar 

  9. Moreau L., Aeyels D. (1999) Local approximations in stability analyis. In preparation

    Google Scholar 

  10. P. Morin, J.-B. Pomet and C. Samson, Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems via Oscillatory Approximation of Lie Brackets in Closed-Loop. Accepted for publication in SIAM Journal on Control & Optimization.

    Google Scholar 

  11. J.A. Sanders and F. Verhulst, Averaging Methods in Nonlinear Dynamical Systems. Applied Mathematical Sciences, Vol. 59. Springer-Verlag, 1985.

    Google Scholar 

  12. A.R. Teel, J. Peuteman and D. Aeyels, Semi-global practical asymptotic stability and averaging. To appear in Systems and Control Letters

    Google Scholar 

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Author information

Authors and Affiliations

  1. SYSTeMS, Universiteit Gent, Technologiepark 9, B-9052, Zwijnaarde, Belgium

    Luc Moreau & Dirk Aeyels

Authors
  1. Luc Moreau
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  2. Dirk Aeyels
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Editor information

Editors and Affiliations

  1. Dept. of Systems Dynamics, Universiteit Gent, Technologiepark-Zwijnaarde 9, 9052, Gent, Belgium

    Dirk Aeyels (Professor) (Professor)

  2. Laboratoire des Signaux et Systèmes, CNRS, SUPELEC, 91192, Gif-sur-Yvette, France

    Françoise Lamnabhi-Lagarrigue (Docteur d’état) (Docteur d’état)

  3. Dept. of Applied Mathematics, University of Twente, PO Box 217, 7500, Enschede, The Netherlands

    Arjan van der Schaft (Professor) (Professor)

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© 1999 Springer-Verlag London Limited

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Moreau, L., Aeyels, D. (1999). Asymptotic methods in stability analysis and control. In: Aeyels, D., Lamnabhi-Lagarrigue, F., van der Schaft, A. (eds) Stability and Stabilization of Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol 246. Springer, London. https://doi.org/10.1007/1-84628-577-1_11

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  • DOI: https://doi.org/10.1007/1-84628-577-1_11

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-638-7

  • Online ISBN: 978-1-84628-577-6

  • eBook Packages: Springer Book Archive

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