This paper deals with the worst-ease analysis of identification of linear shift-invariant (possibly) infinite-dimensional systems. A necessary and sufficient input richness condition for the existence of robustly convergent identification algorithms in l(1) is given. A closed-loop identification setting is studied to cover both stable and unstable (but BIBO stabilizable) systems. Identification (or modeling) error is then measured by distance functions which lead to the weakest convergence notions for systems such that closed-loop stability, in the sense of BIBO stability, is a robust property. Worst-case modeling error bounds in several distance functions are included.