Separation principle for nonlinear systems: a bilinear approach

Mohamed Hammami; Hamadi Jerbi

International Journal of Applied Mathematics and Computer Science (2001)

  • Volume: 11, Issue: 2, page 481-492
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Hammami, Mohamed, and Jerbi, Hamadi. "Separation principle for nonlinear systems: a bilinear approach." International Journal of Applied Mathematics and Computer Science 11.2 (2001): 481-492. <http://eudml.org/doc/207516>.

@article{Hammami2001,
abstract = {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.},
author = {Hammami, Mohamed, Jerbi, Hamadi},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {bilinear systems; observer; stabilization; nonlinear systems; bilinear system; state observer; separation principle},
language = {eng},
number = {2},
pages = {481-492},
title = {Separation principle for nonlinear systems: a bilinear approach},
url = {http://eudml.org/doc/207516},
volume = {11},
year = {2001},
}

TY - JOUR
AU - Hammami, Mohamed
AU - Jerbi, Hamadi
TI - Separation principle for nonlinear systems: a bilinear approach
JO - International Journal of Applied Mathematics and Computer Science
PY - 2001
VL - 11
IS - 2
SP - 481
EP - 492
AB - 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.
LA - eng
KW - bilinear systems; observer; stabilization; nonlinear systems; bilinear system; state observer; separation principle
UR - http://eudml.org/doc/207516
ER -

References

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  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. Zbl0804.93040
  12. 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. 
  13. Massera J.L. (1956): Contribution to stability theory. -Annals of Mathematics, Vol.64, pp.182-206. Zbl0070.31003
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  15. Vidyasagar M. (1980): On the stabilization of nonlinear systems using state detection. - IEEE Trans. Automat. Contr., Vol.AC-25, pp.504-509. Zbl0429.93046

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