Exponential stabilization of a class of nonlinear systems: a generalized Gronwall-Bellman lemma approach

Ibrahima N'Doye (1) , Michel Zasadzinski (1) , Mohamed Darouach (1) , Nour-Edine Radhy (2) , Abdelhaq Bouaziz (3)

1 CRAN - Centre de Recherche en Automatique de Nancy
2 LMPGI - Laboratoire Mécanique, Productique et Génie Industriel
3 LP2MAT - Laboratoire Physique et Matéeriaux, Microélectronique, Automatique et Thermique

In this paper, stabilizing control design for a class of nonlinear affine systems is presented by using a new generalized Gronwall-Bellman lemma approach. The nonlinear systems under consideration can be non Lipschitz. Two cases are treated for the exponential stabilization~: the static state feedback and the static output feedback. The robustness of the proposed control laws with regards to parameter uncertainties is also studied. A numerical example is given to show the effectiveness of the proposed method.

Mots clés: Nonlinear affine systems; Generalized Gronwall-Bellman lemma; Exponential stabilization; Static state feedback; Static output feedback; Robustness

Domaines: Automatique / Robotique

Ibrahima N'Doye, Michel Zasadzinski, Mohamed Darouach, Nour-Edine Radhy, Abdelhaq Bouaziz. Exponential stabilization of a class of nonlinear systems: a generalized Gronwall-Bellman lemma approach. Nonlinear Analysis: Theory, Methods and Applications, 2011, 74 (18), pp.7333-7341. ⟨10.1016/j.na.2011.07.051⟩. ⟨hal-00651139⟩