Thanks for sharing the paper, I think it would have been nice to start with that. I think it would be much more clear to dispense with the general notation and try to directly implement that model, starting with their simplest specification. A lot of what they present is closed-form results that you don’t need. I think you can write out equations (1) and (2) inside the step function and you should be good to go, no matrices or state-space stuff needed.