For distributed or infinite-dimensional systems, stability raises various difficulties. One anomaly is that there can be two realizations, both approximately reachable and observable, but one is exponentially stable and the other is not (unstable). Another is that even the spectrum is not preserved among such realizations. This paper gives conditions under which stability and spectrum are preserved for approximately reahchable and observable realizations. The results have much bearing on robust controller designs based on external system descriptions, e.g., H-infinity designs.