L<inf>2</inf>-optimal identification of MIMO errors-in-variables models

Abstract

This paper extends an L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -optimal identification method for SISO errors-in-variables models (EIVMs) to cope with a MIMO case. According to the orthogonal decomposition signals for measurements, L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -optimal approximate models are built, in which the system model is described by a normalized right graph symbol (NRGS) and the associated noise model (NM) by its complementary inner factor (OF). The v-gap metric is employed to optimize the system model parameters and thus the minimization problem can be solved by linear matrix inequalities (LMIs). With the estimated system model, the NM can then be obtained from a model transform. Finally, a numerical simulation is given to verify the proposed method.