g_margin gain margin and associated crossover frequency

## Syntax

                [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('c',-1+%s,3+2*%s+%s^2) [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)

h = syslin(0.1,0.04798*%z+0.0464,%z^2-1.81*%z+0.9048); [g ,fr]=g_margin(h); warning("off") show_margins(h) warning("on")

## See also

- p_margin
- show_margins
- repfreq
- black
- bode
- nicholschart
- nyquist