On a method for simplifying linear dynamic systems

Davison and Chidambara have exposed methods [1], [5] for approximating a linear dynamic system of high dimension by a model of lower dimension, neglecting the fast decaying modes associated with eigenvalues of high magnitude. In spite of a number of correspondence items from the authors it is not clear which model should be used since the examples given might as well show that either method is correct or incorrect according to the cases. In fact it will appear in the following that the problem lies in the existence of null eigenvalues and that a modification of Davison's model in that case will solve the problem, at least for step inputs; for general inputs it will also be clear that some care must be taken, which was not evident in the previous papers.