In this article, an analytical method is used to obtain multiple model (MM) forms strictly equivalent to a given nonlinear model. The proposed method induces no information loss, contrary to existing order reduction methods. Several MMs formally equivalent to the initial model may be obtained, due to the intermediate quasi-LPV forms. Thus some criteria are given, using the linear matrix inequality (LMI) formulation, in order to chose the most suitable MM for analysis or control purpose. This method is applied to an activated sludge reactor model.

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Abstract-This paper addresses the exact transformation of nonlinear systems into a multiple model form with unmeasurable premise variables. The multiple model structure serves to treat the observability and the state estimation problem of nonlinear systems. Using a method with no information loss, a nonlinear system is transformed into a multiple model, depending on the choice of premise variables. It is a key point, since it allows to choose, between different multiple model forms, the one that has suitable structure and properties, in order to design an observer. The convergence conditions of the state estimation error are expressed in LMI formulation using the Lyapunov method. These proposals are investigated and applied to the three-tank system.

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