Separation principle for nonlinear systems: a bilinear approach

• Autorzy: Mohamed Ali Hammami , Hamadi Jerbi
• Języki publikacji: 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.

Słowa kluczowe

EN

bilinear systems; observer; stabilization; nonlinear systems

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 2
• Strony: 481-492

Daty

wydano

2001

otrzymano

2000-07-15

poprawiono

2001-02-05

Twórcy

autor

Mohamed Ali Hammami

• Faculty of Sciences of Sfax, Department of Mathematics, Route Soukra BP 802, 3018 Sfax Tunisia

autor

Hamadi Jerbi

• Faculty of Sciences of Sfax, Department of Mathematics, Route Soukra BP 802, 3018 Sfax Tunisia

Bibliografia

• 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.
• Boothby W. and Marino R. (1989): Feedback stabilization of planar nonlinear systems. - Syst. Contr. Lett., Vol.12, pp.87-92.
• Bornard G., Couenne N. and Celle F. (1989): Regularly persistent observers for bilinear systems. - Berlin: Springer, Contr. Inform. Sci., pp.130-140.
• Chabour R. and Hammouri H. (1993): Stabilization of planar bilinear systems using an observer configuration. - Appl. Math. Lett., Vol.6, pp.7-10.
• 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.
• Chabour R. and Vivalda J.C. (1991): Stabilisation des systèmes bilineaires dans le plan par une commande non reguliere. - Proc. European Control Conference, ECC'91, Grenoble, France, pp.485-487.
• 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.
• 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.
• Hahn W. (1967) Stability of Motion. -Berlin: Springer.
• 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.
• 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.
• Jerbi H. (1994): Quelques resultats sur la stabilization des systèmes non lineaires par estimation et retour d'etat. -Ph.D. Thesis, University of Metz, France.
• Massera J.L. (1956): Contribution to stability theory. -Annals of Mathematics, Vol.64, pp.182-206.
• Seibert P. and Suarez R. (1990): Global stabilization of nonlinear cascade systems. - Syst. Contr. Lett., Vol.14, pp.347-352.
• Vidyasagar M. (1980): On the stabilization of nonlinear systems using state detection. - IEEE Trans. Automat. Contr., Vol.AC-25, pp.504-509.