# doubt on application of stability criteria

I have only seen systems with this transfer function treated in stability criteria with this general form:$$\frac{KG(s)}{1\pm KG(s)}$$ so the $$\lvert H(s)\rvert =1$$ is it possible to apply criteria with H(s) distinct of 1? or must do some transformation before? thanks.

• Normally, the system TF is assumed in the form: $\frac{KG(s)}{1+KG(s)H(s)}$, and there is no such restriction on $H(s)$. Give a link to the website that you are quoting from – Chu Jan 7 '17 at 9:29
• cranck, do you expect that we should guess what you mean with H(s)? At least, you should show us an equation not only a simple expression. – LvW Jan 7 '17 at 9:48
• This is only valid for systems with Unity feedback path if your systems feedback path has a value that is not equal to one then the system transfer function should be $$\frac{KG(s)}{1+H(s) *KG(s)}$$ – Elbehery Jan 7 '17 at 10:43
• Can you tell us which "stability criteria" are you talking about? Certainly all I know are applicable to H(s) distinct from 1. – Deep Dec 26 '17 at 16:41

If we assume G(s) is strictly positive thus: $$\frac{KG(s)}{1+KG(s)}$$ $$H(s) = 1$$ is a closed loop negative feedback system where it is assumed that H(s) which is the feedback component which is equal to 1.
$$\frac{KG(s)}{1+K H(s)G(s)}$$ $$H(s)\neq 1$$
Basically if you look a Root Locus diagram of a system all the poles should be in the left half plane and the phase plot should be within $\pm\pi$ but thats not strictly true. A system can have range for which K the system is stable.