Reachability, observability, and discretization

It is shown that a commonly used discretization method leads to a certain infidelity regarding the reachability and observability properties of the original versus the discretized version. In a digital implementation this infidelity is amplified due to round off errors. In particular, the reduced order modeling is shown to be very sensitive. A new discretization method of high fidelity is proposed. As an application the commutativity of reduced order modeling and discretization is studied for balanced realizations and a criterion for determining the stepsize corresponding to a certain degree of fidelity is presented.