State estimation of the three-tank system using a multiple model

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.