Minimum and Non-minimum Phase Systems

What are these systems?

For a given magnitude response, there exists multiple transfer functions that can produce that same magnitude response exactly.
However, those transfer functions would produce different phase responses (by adding more phase delay to the inputs)

There is only one minimum phase system for a given magnitude response, but there are an infinite amount of non-minimum phase systems that have the same magnitude response but add different amounts of phase delays
The system whose phase response is the minimum for a given magnitude response is called the minimum phase system (that is like saying: this is the system that can produce this magnitude response with the minimum amount of phase delay added to the inputs)
Other systems are called non-minimum phase systems

Adding a pure time delay: magnitude response is affected by steady state value. If a system has an added extra pure time delay, its magnitude response will not change, but its phase response will be changed (phase delay increases)
- The bad thing about pure time delay or transport lag is that its phase delay increases with frequency and approaches $- \infty$ as $ω \to \infty$
Moving one or more zeros to the RHP: RHP zeros means negative $s$ . A negative $s$ is like a negative derivative. This negative derivative "fights" the input signal by trying to go to the other direction. This "fight" adds a delay to the system
- Systems with RHP initially respond opposite to the input signal then correct themselves to arrive at the desired value at steady state (see the resources below for examples)