[jbay808]

This is a very important application and a tougher problem than most would guess. There is a huge variety of ways to numerically implement even a simple transfer function, and they can have very different consequences in terms of rounding and overflow. Especially if you want to not only guarantee that it converges to a steady-state, but furthermore that the steady-state has no error. I spent a lot of time working on this problem for nanometre-accurate servo controls. Floating and fixed point each have advantages depending on the nature and dynamic range of the variable (eg. location parameter vs scale parameter).