The transfer function, H(jw), equaling to Y/U, is a frequency domain representation of the system’s input-output relationship.
where
It can be derived directly from the state-space matrices A, B, C, and D.
It’s a matrix transfer function if we have multiple inputs and outputs (MIMO). In the SISO case, it becomes a scalar function.
Lets analyze this:
- H is in complex domain. U is in complex domain.
- cos(ωt + ∠H(jω) + ∠U(jω)): The output is a cosine wave with the original frequency (ω) but with a phase shift equal to the sum of the phase shifts introduced by the system and the input signal.