Geodesic
Separation principle for nonlinear systems using a bilinear approximation
Kybernetika, Tome 37 (2001) no. 5, pp. 565-573 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.
In this paper, we study the local stabilization problem of a class of planar nonlinear systems by means of an estimated state feedback law. Our approach is to use a bilinear approximation to establish a separation principle.
Classification : 93C10, 93D15
Keywords: nonlinear system; stabilization problem; feedback; bilinear approximation 
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Hammami, Mohamed Ali; Jerbi, Hamadi. Separation principle for nonlinear systems using a bilinear approximation. Kybernetika, Tome 37 (2001) no. 5, pp. 565-573. http://geodesic.mathdoc.fr/item/KYB_2001_37_5_a2/

[1] Baccioti A., Boieri P.: A characterization of single input planar bilinear systems which admit a smooth stabilizer. Systems Control Lett. 16 (1991), 139–143 | DOI

[2] Boothby W., Marino R.: Feedback stabilization of planar nonlinear systems. Systems Control Lett. 12 (1989), 87–92 | DOI | MR | Zbl

[3] Chabour R., Hammouri H.: Stabilization of planar bilinear systems using an observer configuration. Appl. Math. Lett. 6 (1993), 7–10 | DOI | MR | Zbl

[4] Chabour R., Sallet, G., Vivalda J. C.: Stabilization of nonlinear two dimensional systems: a bilinear approach. Math. Control Signals Systems 9 (1996), 224–246 | MR

[5] Chabour R., Vivalda J. C.: Stabilisation des systemes bilineaires dans le plan par une commande non reguliere. In: Proc. European Control Conference, ECC’91, Grenoble 1991, pp. 485–487 | MR

[6] Čelikovský S.: On the global linearization of bilinear systems. Systems Control Lett. 15 (1990), 433–439 | DOI | MR | Zbl

[7] Dayawansa W. P., Martin C. F., Knowles G.: Asymptotic stabilization of a class smooth two-dimensional systems. SIAM J. Control Optim. 28 (1990), 1321–1349 | DOI | MR

[8] Gauthier J. P., Kupka I.: A separation principle for bilinear systems with dissipative drift. IEEE Trans. Automat. Control AC–37 (1992), 12, 1970–1974 | DOI | MR | Zbl

[9] Hahn W.: Stability of Motion. Springer–Verlag, Berlin 1967 | MR | Zbl

[10] Hammami M. A.: Stabilization of a class of nonlinear systems using an observer design. In: Proc. 32nd IEEE Conference on Decision and Control, San Antonio 1993, Vol. 3, pp. 1954–1959

[11] Hammami M. A., Jerbi H.: On the stabilization of homogeneous cubic vector fields in the plane. Appl. Math. Lett. 7 (1994), 4, 95–99 | DOI | MR

[12] Jerbi H.: Quelques resultats sur la stabilization des systèmes non linéaires par estimation et retour d’état. Doctorat de l’université de Metz 1994

[13] Jerbi H., Hammami M. A., Vivalda J. C.: On the stabilization of homogeneous affine systems. In: 2nd IEEE M.S.N.D. Automat. Control, Chania 1994, pp. 319–326

[14] Massera J. L.: Contribution to stability theory. Ann. of Math. 64 (1956), 182–206 | DOI | MR

[15] Seibert P., Suarez R.: Global stabilization of nonlinear cascade systems. Syst. Control Lett. 14 (1990), 347–352 | DOI | MR | Zbl

[16] Vidyasagar M.: On the stabilization of nonlinear systems using state detection. IEEE Trans. Automat. Control AC–25 (1980), 504–509 | DOI | MR | Zbl