On the Identification and Approximation of Linear Systems

Sammanfattning: This thesis consists of four parts. In the first one, the connections between system identification and model reduction are discussed. The second part deals with the problem of estimating ARMA models for narrow band processes. In the third part we study how to build models of continuous time dynamical models form discrete time measurements, and in the fourth part we show how to affect the bias distribution in transfer function estimation.No mathematical models are perfect descriptions of physical systems. Recently there has been a growing interest in how approximate models will affect the results, in e.g. control design. System identification deals with the problem of building mathematical models of dynamical systems based on observed data from the system. The theme of this thesis is to study how the fact that the physical system cannot be exactly represented within the chosen model set will influence the identified model.In parts I and II the application of model reduction in system identification is investigated. It is showed how the fact that the high order model is obtained from an identification experiment will affect the choice of model reduction procedure. A by-product will be an identification algorithm based on an high order ARX estimate and model reduction.In part III the problem of building models of continuous time linear dynamical systems based on discrete time observations of the system is considered. By studying continuous time prediction error methods it is shown how the choice of model structure and sampling interval will affect the resulting estimate in case of fast sampling.In part IV it is shown how the use of prefilters, noise model, sampling interval and prediction horizon will affect the distribution of bias transfer function estimation. An important aspect is that the true sytem is not assumed to be exactly represented within the chosen model set. It is shown how the distribution of bias in the frequency domain is governed by a weighting function that emphasizes different frequency bands.