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Let us consider a linear time-invariant system. The term minimum phase is used for a system that has stable poles and stable zeros. A system is called nonminimal phase if it is not minimum phase.

The problem that I have is that these definitions do not make it clear if a system with one pole or one zero which has a real part of zero is still called minimal phase or not.

Is there some reference that is giving a clear definition of the term minimal phase?

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    \$\begingroup\$ Did you read the Wikipedia article on minimum phase? Is there a specific part that we could help to explain better? \$\endgroup\$ – The Photon Nov 14 '17 at 19:11
  • \$\begingroup\$ The first link in google explains well. #wikipedia \$\endgroup\$ – Mitu Raj Nov 14 '17 at 19:16
  • \$\begingroup\$ I believe, a 1st order transfer function will always be stable and causal and thus meets the criteria. It is when there is feedback with higher orders that systems can become unstable when there is excess delay and gain at that frequency (Barkhausen Criteria). we consider good phase margin as 60 deg. and poor phase margin <20 deg due to ringing and overshoot. But non-minimum implies the negative feedback phase delay turns in positive feedback with gain >1 \$\endgroup\$ – Sunnyskyguy EE75 Nov 14 '17 at 19:25
  • \$\begingroup\$ If a transfer function contains poles or/and zeros located in the right half-plane or includes pure delays, then the transfer function is non-minimum phase and Bode criteria for stability must be used with caution. When minimum phase, you can deduce the magnitude of a given system from its phase asymptotic response and vice versa (Kramers-Kronig). When the system features RHP zeros and/or poles or delays, it no longer works. \$\endgroup\$ – Verbal Kint Nov 14 '17 at 19:31
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    \$\begingroup\$ Yes, a pole on the imaginary axis would indicate an unbounded output for a bounded input (a sine with the corresponding frequency). \$\endgroup\$ – The Photon Nov 14 '17 at 22:41
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these definitions do not make it clear if a system with one pole or one zero which has a real part of zero is still called minimal phase or not.

First, from the Wikipedia article Minimum Phase:

a linear, time-invariant system is said to be minimum-phase if the system and its inverse are causal and stable.

And from the article BIBO Stability:

For a rational and continuous-time system ... all poles of the system must be in the strict left half of the s-plane for BIBO stability.

It makes sense that a system with a pole on the imaginary axis is not considered stable, since that pole would mean that a bounded input (a sinusoid) would produce an unbounded output.

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