State estimation of nonlinear discrete-time systems based on the decoupled multiple model approach

Multiple model approach is a powerful tool for modelling nonlinear systems. Two structures of multiple models can be distinguished. The first structure is characterised by decoupled submodels, i.e. with no common state (decoupled multiple model), in opposition to the second one where the submodels share the same state (Takagi-Sugeno multiple model). A wide number of research works investigate the state estimation of nonlinear systems represented by a classic Takagi-Sugeno multiple model. On the other hand, to our knowledge, the state estimation of the decoupled multiple model has not been investigated extensively. This paper deals with the state estimation of nonlinear systems represented by a decoupled multiple model. Conditions for ensuring the convergence of the estimation error are formulated in terms of a set of Linear Matrix Inequalities (LMIs) employing the Lyapunov direct method.