I wanted to clear this doubt I have since a long time and for which I am not able to find a clear answer since different sources say differently or ambiguously.
$\textbf{Does a system have to be stable to be minimum phase?}$ By definition, does a minimum phase system require stability or just Left Half Plane zeros?
Thank you in advance!
On
The above is one definition. An alternative definition, also used in the literature, is that a continuous-time transfer function is stable if the poles have negative real part, and minimum-phase if the zeros have negative real part. With the latter definition, the concepts of stability and minimum-phase are independent. It's a question of taste, which one to adopt.
A minimum-phase system should NOT have any poles or zeros in the open right half of s-plane. This effectively imply that the minimum-phase system has to be at least Lyapunov stable if not asymptotically stable.