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# g_margin

gain margin and associated crossover frequency

### Syntax

gm=g_margin(h) [gm,fr]=g_margin(h)

### Arguments

- h
a SISO linear system (see :syslin).

- gm
a number, the gain margin (in dB) if any of

`Inf`

- fr
a number, the associated frequency in hertz, or an empty matrix if the gain margin does not exist.

### Description

Given a SISO linear system in continuous or discrete time,
`g_margin`

returns `gm`

, the
gain margin in dB of `h`

and
`fr`

, the achieved corresponding frequency in
Hz.

The gain margin, if it exists, is the minimal value of the
system gain at points where the nyquist plot crosses the negative
real axis. In other words the gain margin is
`20*log10(1/g)`

where `g`

is the
open loop gain of `h`

when the frequency response
phase of `h`

equals -180°

The algorithm uses polynomial root finder to solve the equations:

- h(s)=h(-s)
for the continuous time case.

- h(z)=h(1/z)
for the discrete time case.

### Examples

h=syslin('c',-1+%s,3+2*%s+%s^2) //continuous time case [g,fr]=g_margin(h) [g,fr]=g_margin(h-10) nyquist(h-10)

h = syslin(0.1,0.04798*%z+0.0464,%z^2-1.81*%z+0.9048);//discrete time case [g ,fr]=g_margin(h); show_margins(h)

### See also

- p_margin — phase margin and associated crossover frequency
- show_margins — display gain and phase margin and associated crossover frequencies
- repfreq — frequency response
- black — Black-Nichols diagram of a linear dynamical system
- bode — Bode plot
- nicholschart — Nichols chart
- nyquist — nyquist plot

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