The system with the open loop transfer function G(s) H(s)

The system with the open loop transfer function G(s) H(s) = 1 has a gain margin of
s(s² + s + 1)

∠ G(jω) H(jω) = – 180°

= -90° - tan^{– 1}	ω
	1 - ω²

since G(jω) H(jω) =		1
		jω(jω + 1 - ω²)

⇒ tan^{– 1}	ω	= 90°
	1 - ω²

K > 0
∴ ω = 1 rad / sec
Then, GM = – log|G(jω), H(jω )| _{ω = 1} | = 0 dB

The system with the open loop transfer function G(s) H(s) =	1	has a gain margin of
	s(s² + s + 1)