Filter-based Approximated Models for Discrete-time Systems. Application to Multirate Sampled LTI Systems

This paper deals with the task of obtaining approximated models of discrete-time systems by the use of parametrical identification algorithms. Firstly, a filter-based identification method used to obtain a parametric model from a series data of the impulse of the system based in Leverrier’s algorithm is revised. A second method based on least squares minimization that allows identifying the discrete system from input-output data is also presented. These techniques are of particular practical interest when treating discrete-time systems where the analytical resolution becomes very complex or even unfeasible. This is the case of the problem presented in the examples, where a multirate sampling technique is used to discretize the system under real sampling. This strategy yields a better description than that obtained using the traditional sampling method, but it involves a difficult treatment of parametrical model in terms of the poles and zeros due to the complexity of the resulting discrete transfer functions, but where a measured data series of the output is available. Key-Words: Modeling, Discrete-time systems, System identification, Multirate sampling, LTI (linear time invariant) systems.