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Separation Principle for Nonlinear Systems: a Bilinear Approach

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EN
Abstrakty
EN
In this paper we investigate the local stabilizability of single-input nonlinear affine systems by means of an estimated state feedback law given by a bilinear observer. The associated bilinear approximating system is assumed to be observable for any input and stabilizable by a homogeneous feedback law of degree zero. Furthermore, we discuss the case of planar systems which admit bad inputs (i.e. the ones that make bilinear systems unobservable). A separation principle for such systems is given.
Twórcy
  • Faculty of Sciences of Sfax, Department of Mathematics, Route Soukra BP 802, 3018 Sfax, Tunisia
autor
  • Faculty of Sciences of Sfax, Department of Mathematics, Route Soukra BP 802, 3018 Sfax, Tunisia
Bibliografia
  • [1] Baccioti A. and Boieri P. (1991): A characterization of single input planar bilinear systems which admit a smooth stabilizer. - Syst. Contr. Lett., Vol. 16, pp. 139-143.
  • [2] Boothby W. and Marino R. (1989): Feedback stabilization of planar nonlinear systems. - Syst. Contr. Lett., Vol. 12, pp. 87-92.
  • [3] Bornard G., Couenne N. and Celle F. (1989): Regularly persistent observers for bilinear systems. - Berlin: Springer, Contr. Inform. Sci., pp. 130-140.
  • [4] Chabour R. and Hammouri H. (1993): Stabilization of planar bilinear systems using an observer configuration. - Appl. Math. Lett., Vol. 6, pp. 7-10.
  • [5] Chabour R., Sallet G. and Vivalda J.C. (1996): Stabilization of nonlinear two dimensional systems: A bilinear approach. - Math. Contr. Signal Syst., pp. 224-246.
  • [6] Chabour R. and Vivalda J.C. (1991): Stabilisation des systèmes bilinéaires dans le plan par une commande non réguliere. - Proc. European Control Conference, ECC’91, Grenoble, France, pp. 485-487.
  • [7] Dayawansa W.P., Martin C.F. and Knowles G. (1990): Asymptotic stabilization of a class smooth two-dimensional systems. - SIAM J. Contr. Optim., Vol. 28, pp. 1321-1349.
  • [8] Gauthier J.P. and Kupka I. (1992): A separation principle for bilinear systems with dissipative drift. - IEEE Trans. Automat. Contr., Vol. AC-37, No. 12, pp. 1970-1974.
  • [9] Hahn W. (1967) Stability of Motion. - Berlin: Springer.
  • [10] Hammami M.A. (1993): Stabilization of a class of nonlinear systems using an observer design. - Proc. 32nd IEEE Conf. Decision and Control, San Antonio, Texas, Vol. 3, pp. 1954-1959.
  • [11] Hammami M.A. and Jerbi H. (1994): On the stabilization of homogeneous cubic vector fields in the plane. - Appl. Math. Lett., Vol. 7, No. 4, pp. 95-99.
  • [12] Jerbi H. (1994): Quelques résultats sur la stabilization des systèmes non linéaires par estimation et retour d’état. - Ph.D. Thesis, University of Metz, France.
  • [13] Massera J.L. (1956): Contribution to stability theory. - Annals of Mathematics, Vol. 64, pp. 182-206.
  • [14] Seibert P. and Suarez R. (1990): Global stabilization of nonlinear cascade systems. - Syst. Contr. Lett., Vol. 14, pp. 347-352.
  • [15] Vidyasagar M. (1980): On the stabilization of nonlinear systems using state detection. - IEEE Trans. Automat. Contr., Vol. AC-25, pp. 504-509.
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bwmeta1.element.baztech-article-BPZ1-0012-0021
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