Factoring the Update Function

The update function has the form

update:  Reals ^N  ´ Reals ^M  ® Reals ^N ´ Reals ^K

We factor this into two functions:

update = (nextState, output)

such that for all s Î States and x Î Inputs,

update(s, x) = (nextState(s, x), output(s, x))

The nextState function has the form

nextState:  Reals ^N  ´ Reals ^M  ® Reals ^N

The output function has the form

output:  Reals ^N  ´ Reals ^M  ® Reals ^K