On structural property metrics for Model Error of linear systems

Controllability Margin (CM) and Observability Margin (OM) for linear systems, including Linear Time Invariant (LTI) and Linear Time Varying (LTV) systems are defined from the view of singular perturbation and regular perturbation, and the corresponding assessment methods are established. Based on the CM, OM and the recently introduced Singular Perturbation Margin (SPM) and Generalized Gain Margin (GGM), the concept of Model Error Structure (MES) is provided as a structural property metric for linear systems. The results in this paper are illustrated by the examples of a flexible beam and Hill equations.