Pi Observer Design for Discrete-time Decoupled Multiple Models

This paper deals with the state estimation of nonlinear systems. Our approach is based on the representation of a nonlinear system with the help of a decoupled multiple model. This kind of multiple model constitutes an alternative to the classic Takagi-Sugeno multiple model. Indeed, in opposition to this last, in the decoupled multiple model the dimension (i.e. the number of states) of the submodels may be different. In order to cope with the state estimation problem a Proportional-Integral observer (PIO) is designed. Indeed, in contrast to the classic Proportional observer the PIO is known by its robustness properties. Sufficient conditions for ensuring the estimation error convergence are given in LMI form.