I'm not sure if I'm missing something really obvious here.

I can simulate a system given a complete input time series using control.lsim().

But how can I simulate a system where I get the samples one at a time and want to know the output after each one? For instance, if I'm using it to control something or process audio or whatever?

The best I've come up with so far is to convert it to a state-space representation (if it isn't already), discretise it using the sample() function (again, if it isn't already) and manually run the system equations. Is there not some way of doing this built in?