Observer for Lipschitz nonlinear systems: mean value theorem and sector nonlinearity transformation

Dalil Ichalal (1) , Benoît Marx (2) , Said Mammar (1) , Didier Maquin (2) , José Ragot (2)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 CRAN - Centre de Recherche en Automatique de Nancy

In this paper, the problem of observer design for nonlinear Lipschitz systems is treated. An emphasis is put on maximizing the admissible Lipschitz constant for which the observer design is possible. This problem is tackled using a Takagi-Sugeno modeling approach. The idea is to re-write the state estimation error dynamics as an autonomous Takagi- Sugeno system, using the Mean Value Theorem and the sector nonlinearity transformation. The stability of the state estimation error is studied with the Lyapunov theory by using a non- quadratic Lyapunov function and by computing its variation between m consecutive samples. The interest of these manip- ulations is to obtain LMI conditions admitting solutions for large values of the Lipschitz constant. Finally, two examples are provided in order to hilight the performances of the proposed approach.

Domaines: Automatique / Robotique

Dalil Ichalal, Benoît Marx, Said Mammar, Didier Maquin, José Ragot. Observer for Lipschitz nonlinear systems: mean value theorem and sector nonlinearity transformation. IEEE Multi-Conference on Systems and Control, MSC 2012, Oct 2012, Dubrovnik, Croatia. pp.CDROM. ⟨hal-00702669⟩