The open loop transfer function of a unity feedback system

The open loop transfer function of a unity feedback system is given by
G(s) = (e^-0.1s)
s

The gain margin of this system is

Given : G(s) =	e^-0.1s
	s

⇒ G(jω) =	e^-0.1jω
	jω

Phase crossover frequency :

-90 - 0.1 ω ×	180	= - 180
	π

⇒	18	ω = 90
	π

⇒ ω = 5π = 15.7 rad/sec
Gain margin :

a = \|G(jω)\|_{at ω = 18.7} =	1	=	1
	ω		15.7

∴ Gain margin = 20 log a

= 20 log	1	= -23.9 dB
	15.7

G(s) =	(e^-0.1s)
	s