Scenario (plant model subject to process variations)
Consider a plant \$P(s)\$ in series with a controller \$D(s)\$ with a negative feedback path around it, where the closed loop is given by the complementary sensitivity function \$T(s)\$. $$T(s)=\frac{P(s)D(s)}{1+P(s)D(s)}$$
Now consider that the plant model is subject to process variations \$\Delta P\$.
Question (\$ \Delta P \$ relation to complementary sensitivity function for non-minimum phase plant)
I read in a book\$^*\$ that to avoid system instability, the maximum allowable process model variation \$\Delta P(s)\$ must satisfy the following condition\$^*\$ derived from the Nyquist plot of the loop transfer function: $$\frac{|\Delta P(j\omega)|}{|P(j\omega)|}<\frac{1}{|T(j\omega)|}$$ This is derived for a Nyquist contour with no loops around \$-1+0j\$, i.e. a minimum phase system. I was wondering how this condition would apply to a non-minimum phase system, i.e. one with RHP poles or zeros, and hence with loops around \$-1+0j\$ on the Nyquist plot.
Footnotes for clarification
\$^*\$ This is derived from the Nyquist plot of the loop transfer function \$L(s)=P(s)D(s)\$, and comes from the condition that the magnitude of process variation \$|C\Delta P|\$ is not larger than the magnitude of the vector from \$L(s)\$ to the critical point \$-1 + 0j \$ on the Nyquist plot, or: $$|C\Delta P|<|1+L|$$
\$^*\$ page 192 of https://www.cds.caltech.edu/~murray/courses/cds101/fa02/caltech/astrom-ch5.pdf
