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In this paper, model-based LQG control with impedance tomographic measurements is discussed. Impedance tomography is a difficult class of inverse ill-posed problems, which in the case of control system design, means that the computation of the state estimates is an unstable problem. It is shown with simulations that accurate stochastic modelling of the state and observation models may facilitate stable state estimation, which in turn facilitates feedback control. When the state evolution model is based on partial differential equations, the price is that the dimension of the state is invariably very large, since state reduction leads to intolerable approximation errors.