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On The Stabilization of Homogeneous Perturbed Systems

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Abstract

In this paper, using some results on manifolds, we establish some conditions for stabilization of single-input homogeneous by dilation systems.

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References

  1. V. Andriano, Global feedback stabilization of the angular velocity of a symmetric rigid body. Syst. Control Lett. 10 (1988), p. 251–256.

    Article  Google Scholar 

  2. Z. Artstein, Stabilization with relaxed controls. Nonlinear Anal. Theory Meth. Appl. 7 (1983), 1163–1173.

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Bacciotti, Local stabilizability of nonlinear control systems. Ser. Adv. Math. Appl. Sci. 8, World Scientific, Singapore–River Edge–London (1992).

  4. J. M. Coron and L. Praly, Adding an integrator for the stabilization problem. Syst. Control Lett. 17 (1991), 89–104.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Faubourg and J.-B. Pomet, Control Lyapunov functions for homogeneous Jurdjevic–Quinn systems. ESAIM Control, Optim. Calc. Var. 5 (2000), 293–311.

    Article  MATH  MathSciNet  Google Scholar 

  6. H. Jerbi, A manifold-like characterization of asymptotic stabilizability of homogeneous systems. Syst. Control Lett. 41 (2002), 173–178.

    Article  MathSciNet  Google Scholar 

  7. H. Jerbi and T. Kharrat, Only a level set of a control Lyapunov function for homogeneous systems. Cybernetika 41 (2005), No. 5, 593–600.

    MathSciNet  Google Scholar 

  8. M. Kawski, Homogeneous stabilizing feedback laws. Control Theory Adv. Tech. 6 (1990), 497–516.

    MathSciNet  Google Scholar 

  9. S. Lefschetz, Stability of nonlinear control systems. Academic Press, New York (1965).

    MATH  Google Scholar 

  10. L. Rosier, Homogeneous Lyapunov function for homogeneous continuous vector field. Syst. Control Lett. 19 (1992), 467–473.

    Article  MATH  MathSciNet  Google Scholar 

  11. E. D. Sontag, A “universal” construction of Artstein’s theorem on nonlinear stabilization. Syst. Control Lett. 13 (1989), No. 2.

    Google Scholar 

  12. J. Tsinias, Stabilization of affine in control nonlinear systems. Nonlinear Anal. Theory Meth. Appl. 12 (1988), 1283–1296.

    Article  MATH  MathSciNet  Google Scholar 

  13. J. Tsinias, Sufficient Lyapunov-like conditions for stabilization. Math. Contr. Signals Syst. 2 (1989), 343–357.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Tsinias, Remarks on feedback stabilizability of homogeneous systems. Control Theory Adv. Tech. 6 (1990), 533–542.

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculté des sciences de Sfax, Département de Math, Route Soukra Km 4 3018 BP 802, Sfax, Tunisie

    Hamadi Jerbi, Wajdi Kallel & Thouraya Kharrat

Authors
  1. Hamadi Jerbi
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  2. Wajdi Kallel
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  3. Thouraya Kharrat
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Correspondence to Hamadi Jerbi.

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Jerbi, H., Kallel, W. & Kharrat, T. On The Stabilization of Homogeneous Perturbed Systems. J Dyn Control Syst 14, 595–606 (2008). https://doi.org/10.1007/s10883-008-9053-9

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  • DOI: https://doi.org/10.1007/s10883-008-9053-9

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