L 2 -optimal identification of errors-in-variables models based on normalised coprime factors

Abstract

A frequency-domain method is proposed to cope with errors-in-variables model (EIVM) identification when the input and output noises are bounded by a certain upper bound. Based on normalised coprime factor model (NCFM) description, L2-optimal approximate models for an EIVM are first established, which consist of a system NCFM and its complementary inner factor model (CIFM) characterising the noises. Then the v-gap metric criterion is minimised to optimise a system coprime factor model, from which the system NCFM can be obtained by normalisation. During the optimisation, a priori information on the system poles can be fully used to reduce the overfitting effect caused by the noises. The associated noise CIFM can be readily constructed from the resulting estimated system NCFM by a model transformation. Compared with related identification methods, the system model can be effectively solved by linear matrix inequalities and the associated noise model can then be directly built. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed method.