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Week 6

• Infinite state
• Factoring
• Update
• Time
• Differential eqns
• Linear Functions
• LTI systems
• State response
• Output response
• Convolution

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 ∈ States and x ∈ 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