Software for Approximate Linear System Identification

The main features of the considered identification problem are that there is no a priori separation of the variables into inputs and outputs and the approximation criterion, called misfit, is representation invariant. The misfit is defined as the minimum of the l2-norm between the given time series and a time series that is consistent with the approximate model. The misfit is equal to zero if and only if the model is exact and the smaller the misfit is (by definition) the more accurate the model is. The considered model class consists of all linear time-invariant systems of bounded complexity and the complexity is specified by the number of inputs and the smallest number of lags in a difference equation representation. We present a MATLAB function for approximate identification based on misfit minimization. Although the problem formulation is representation independent, we use an input/state/output representation of the identified system in order to allow maximum compatibility with other software packages for system identification, analysis, and design.