thanks t_n_k,It is infinite - the total phase shift tends to exactly 180° as the frequency tends to infinity at which point the transfer gain is infinitesimal.
Consider a [2nd order?] transfer function likethanks t_n_k,
erm, is that every second order system will cause infinity gain margin?
thanks t_n_K, i got itConsider a [2nd order?] transfer function like
\(G(s)=\frac{(10-s)}{s(s+5)}\)
Which has a non-infinite gain margin but has an unbounded step response.
Considered in isolation, gain margin of itself doesn't tell us much about system stability - so a system could have an infinite gain margin but be unstable or unbounded in transient response.
For instance the transfer function
\(G(s)=\frac{0.3}{{(s-0.001)}^2+0.09}\)
has infinite gain margin but has an unstable step response.