S-functions can include parameter inputs. There are examples of this for Level 2 MATLAB S-function, (msfcndemo_limintm) and C-MEX S-functions, (see sfundemos).
In a Level 2 MATLAB S-function, during "setup" set the number of dialog parameters:
Anywhere you need to reference a parameter (for example) inside "InitConditions" you can access it through the block object:
block.ContStates.Data = block.DialogPrm(3).Data;
The parameters are passed into the block through the S-function block parameters, separated by commas.
For C-MEX S-functions, use ssSetNumSfcnParams in mdlInitializeSizes to set the number of parameters and ssGetSfcnParam to get a pointer to an mxArray anywhere you need to use it. C-MEX S-functions also need to do some parameter checking, so it can get a lot more complicated. See the SFCNDEMOS for examples.