# On $H_\infty$ norm for transfer function

For a given scenario in the context of control system, I'm trying to investigate how the $$H_\infty$$ norm can be calculated for a transfer function as follows:
$$G(s)= \frac{w_n^2}{s^2 +2\zeta w_ns +w_n^2 }$$

$$\left \| G \right \| _\infty = \max \limits _{\omega} |G(j\omega)|$$

$$\left \| G \right \| _\infty = \sup \limits _{\omega} |G(j\omega)|$$

I know how to deal with such problems when the case is specific one, for example the frequency value is known. However, I get confused with this general case. any idea

• Can you try to formulate a specific question? I'm not sure what you're asking us. – Marcus Müller Feb 27 '19 at 9:25
• So, what is the specific question you're asking? I'm really not sure what you need help with! What's the first step that you don't know how to do? – Marcus Müller Feb 27 '19 at 11:51
• That's not specific. – Marcus Müller Feb 27 '19 at 12:27
• Can you say what you don't understand about your max and sup formulas? I mean, the answer for "what do I need to calculate" is given by these formulas, explicitly. – Marcus Müller Feb 27 '19 at 12:39
• – MBaz Feb 27 '19 at 16:12