International audienceIn this paper, a proportional integral (PI) and a proportional multiple integral observer (PMI) are proposed in order to estimate the state and the unknown inputs of nonlinear systems described by a Takagi-Sugeno model with unmeasurable premise variables. This work is an extension to nonlinear systems of the PI and PMI observers developed for linear systems. The state estimation error is written as a perturbed system. First, the convergence conditions of the state estimation errors between the system and each observer are given in LMI (Linear Matrix Inequality) formulation. Secondly, a comparison between the two observers is made through an academic example

International audienceThis work is dedicated to the synthesis of a new fault detection and identification scheme for the actuator and/or sensor faults modeled as unknown inputs of the system. The novelty of this scheme consists in the synthesis of a new structure of proportional-integral observer (PIO) reformulated from the new linear ARX-Laguerre representation with filters on system input and output in order to estimate the unknown inputs presented as faults. The designed observer exploits the input/output measurements to reconstruct the Laguerre filter outputs where the stability and the convergence properties are ensured by using Linear Matrix Inequality. However, a significant reduction of this model is subject to an optimal choice of both Laguerre poles which is achieved by a new proposed identification approach based on a genetic algorithm. The performances of the proposed identification approach and the resulting PIO are tested on numerical simulation and validated on a 2nd order electrical linear system