Analysis of linear dynamic systems of low rank

Abstract

Abstract We present here procedures of how obtain stable solutions to linear dynamic systems can be found. Different types of models are considered. The basic idea is to use the H-principle to develop low rank approximations to solutions. The approximations stop, when the prediction ability of the model cannot be improved for the present data. Therefore, the present methods give better prediction results than traditional methods that give exact solutions. The vectors used in the approximations can be used to carry out graphic analysis of the dynamic systems. We show how score vectors can display the low dimensional variation in data, the loading vectors display the correlation structure and the transformation (causal) vectors how the variables generate the resulting variation in data. These graphics methods are important in supervising and controlling the process in light of the variation in data.