As is well-known, there are always discrepancies between design models and the actual physical systems or phenomena that they model. These discrepancies can be due to several factors including the approximation of complex models by simpler ones, the presence of unavoidable experimental errors when collecting data, or even due to unknown or unmodeled effects. Regardless of their source, such perturbations can degrade the performance of otherwise optimal designs. Examples to this effect abound in the fields of signal and image processing, digital communications, control, and others.
These possibilities have motivated over the years numerous investigations on robust design techniques that are less sensitive to such perturbations including, among others, total-least-squares methods and H_oo methods. In this work, we provide an overview of research efforts on design strategies for models and data with bounded perturbations. In comparison to TLS and H_oo methods, the resulting design procedures perform data regularization as opposed to de-regularization; they are based on robust regularized least-squares formulations. Applications in state-space estimation for models with parameteric uncertainties will be discussed.