and hence is stable. Note that the fact that PM>0 implies that $T(j\overline{\omega})<1$, where $\overline{\omega}$ is the frequency at which $\text{arg}(T(j\overline{\omega}))=\pi $, that is, the gain margin is also positive.

From Equation 67 it follows that

$\text{arg}(T(j{\omega}_{c}))={\omega}_{c}{T}^{+}+{\mathrm{tan}}^{-1}\frac{{\omega}_{c}}{K}+{\mathrm{tan}}^{-1}\frac{{\omega}_{c}}{2{N}^{-}/C{({T}^{+})}^{2}}+{\mathrm{tan}}^{-1}\frac{{\omega}_{c}}{1/{T}^{+}}$ (73)

Since

${\omega}_{c}=0.1\mathrm{min}\left\{\frac{2{N}^{-}}{{({T}^{+})}^{2}C},\frac{1}{{T}^{+}}\right\}$

it follows that

${\omega}_{c}{T}^{+}=0.1\mathrm{min}\left\{\frac{2{N}^{-}}{{T}^{+}C},1\right\}$

so that ...

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